diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0b484e06013..67b0153053a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,9 @@
 
 ## Apollo Client (vNEXT)
 
+- In all Apollo Client packages, the compilation of `lib/bundle.esm.js` to `lib/bundle.cjs.js` and `lib/bundle.umd.js` now uses Babel instead of Rollup, since Babel correctly compiles some [edge cases](https://github.com/apollographql/apollo-client/issues/4843#issuecomment-495717720) that neither Rollup nor TypeScript compile correctly. <br/>
+  [@benjamn](https://github.com/benjamn) in [#4911](https://github.com/apollographql/apollo-client/pull/4911)
+
 ### Apollo Cache In-Memory
 
 - Pretend that `__typename` exists on the root Query when matching fragments. <br/>
diff --git a/config/rollup.config.js b/config/rollup.config.js
index a0dda885253..e3a1a16bf40 100644
--- a/config/rollup.config.js
+++ b/config/rollup.config.js
@@ -2,6 +2,10 @@ import nodeResolve from 'rollup-plugin-node-resolve';
 import typescriptPlugin from 'rollup-plugin-typescript2';
 import typescript from 'typescript';
 import path from 'path';
+import fs from 'fs';
+import { transformSync } from '@babel/core';
+import cjsModulesTransform from '@babel/plugin-transform-modules-commonjs';
+import umdModulesTransform from '@babel/plugin-transform-modules-umd';
 import invariantPlugin from 'rollup-plugin-invariant';
 import { terser as minify } from 'rollup-plugin-terser';
 
@@ -49,29 +53,14 @@ export function rollup({
     return './lib/' + outputPrefix + '.' + format + '.js';
   }
 
-  function convert(format) {
+  function fromSource(format) {
     return {
-      input: outputFile('esm'),
+      input,
       external,
       output: {
         file: outputFile(format),
         format,
         sourcemap: true,
-        name,
-        globals,
-      },
-      onwarn,
-    };
-  }
-
-  return [
-    {
-      input,
-      external,
-      output: {
-        file: outputFile('esm'),
-        format: 'esm',
-        sourcemap: true,
       },
       plugins: [
         nodeResolve({
@@ -90,14 +79,61 @@ export function rollup({
         }),
       ],
       onwarn,
-    },
-    convert('umd'),
-    convert('cjs'),
+    };
+  }
+
+  function fromESM(toFormat) {
+    return {
+      input: outputFile('esm'),
+      output: {
+        file: outputFile(toFormat),
+        format: 'esm',
+        sourcemap: false,
+      },
+      // The UMD bundle expects `this` to refer to the global object. By default
+      // Rollup replaces `this` with `undefined`, but this default behavior can
+      // be overridden with the `context` option.
+      context: 'this',
+      plugins: [{
+        transform(source, id) {
+          const output = transformSync(source, {
+            inputSourceMap: JSON.parse(fs.readFileSync(id + '.map')),
+            sourceMaps: true,
+            plugins: [
+              [toFormat === 'umd' ? umdModulesTransform : cjsModulesTransform, {
+                loose: true,
+                allowTopLevelThis: true,
+              }],
+            ],
+          });
+
+          // There doesn't seem to be any way to get Rollup to emit a source map
+          // that goes all the way back to the source file (rather than just to
+          // the bundle.esm.js intermediate file), so we pass sourcemap:false in
+          // the output options above, and manually write the CJS and UMD source
+          // maps here.
+          fs.writeFileSync(
+            outputFile(toFormat) + '.map',
+            JSON.stringify(output.map),
+          );
+
+          return {
+            code: output.code,
+          };
+        }
+      }],
+    }
+  }
+
+  return [
+    fromSource('esm'),
+    fromESM('cjs'),
+    fromESM('umd'),
     {
       input: outputFile('cjs'),
       output: {
         file: outputFile('cjs.min'),
-        format: 'cjs',
+        format: 'esm',
       },
       plugins: [
         minify({
diff --git a/package-lock.json b/package-lock.json
index b7f215776ac..5e8d317ce33 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -13,17 +13,17 @@
       }
     },
     "@babel/core": {
-      "version": "7.4.4",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.4.4.tgz",
-      "integrity": "sha512-lQgGX3FPRgbz2SKmhMtYgJvVzGZrmjaF4apZ2bLwofAKiSjxU0drPh4S/VasyYXwaTs+A1gvQ45BN8SQJzHsQQ==",
+      "version": "7.4.5",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.4.5.tgz",
+      "integrity": "sha512-OvjIh6aqXtlsA8ujtGKfC7LYWksYSX8yQcM8Ay3LuvVeQ63lcOKgoZWVqcpFwkd29aYU9rVx7jxhfhiEDV9MZA==",
       "dev": true,
       "requires": {
         "@babel/code-frame": "^7.0.0",
         "@babel/generator": "^7.4.4",
         "@babel/helpers": "^7.4.4",
-        "@babel/parser": "^7.4.4",
+        "@babel/parser": "^7.4.5",
         "@babel/template": "^7.4.4",
-        "@babel/traverse": "^7.4.4",
+        "@babel/traverse": "^7.4.5",
         "@babel/types": "^7.4.4",
         "convert-source-map": "^1.1.0",
         "debug": "^4.1.0",
@@ -34,6 +34,29 @@
         "source-map": "^0.5.0"
       },
       "dependencies": {
+        "@babel/parser": {
+          "version": "7.4.5",
+          "resolved": "https://registry.npmjs.org/@babel/parser/-/parser-7.4.5.tgz",
+          "integrity": "sha512-9mUqkL1FF5T7f0WDFfAoDdiMVPWsdD1gZYzSnaXsxUCUqzuch/8of9G3VUSNiZmMBoRxT3neyVsqeiL/ZPcjew==",
+          "dev": true
+        },
+        "@babel/traverse": {
+          "version": "7.4.5",
+          "resolved": "https://registry.npmjs.org/@babel/traverse/-/traverse-7.4.5.tgz",
+          "integrity": "sha512-Vc+qjynwkjRmIFGxy0KYoPj4FdVDxLej89kMHFsWScq999uX+pwcX4v9mWRjW0KcAYTPAuVQl2LKP1wEVLsp+A==",
+          "dev": true,
+          "requires": {
+            "@babel/code-frame": "^7.0.0",
+            "@babel/generator": "^7.4.4",
+            "@babel/helper-function-name": "^7.1.0",
+            "@babel/helper-split-export-declaration": "^7.4.4",
+            "@babel/parser": "^7.4.5",
+            "@babel/types": "^7.4.4",
+            "debug": "^4.1.0",
+            "globals": "^11.1.0",
+            "lodash": "^4.17.11"
+          }
+        },
         "debug": {
           "version": "4.1.1",
           "resolved": "https://registry.npmjs.org/debug/-/debug-4.1.1.tgz",
@@ -42,6 +65,12 @@
           "requires": {
             "ms": "^2.1.1"
           }
+        },
+        "globals": {
+          "version": "11.12.0",
+          "resolved": "https://registry.npmjs.org/globals/-/globals-11.12.0.tgz",
+          "integrity": "sha512-WOBp/EEGUiIsJSp7wcv/y6MO+lV9UoncWqxuFfm8eBwzWNgyfBd6Gz+IeKQ9jCmyhoH99g15M3T+QaVHFjizVA==",
+          "dev": true
         }
       }
     },
@@ -86,12 +115,45 @@
         "@babel/types": "^7.0.0"
       }
     },
+    "@babel/helper-module-imports": {
+      "version": "7.0.0",
+      "resolved": "https://registry.npmjs.org/@babel/helper-module-imports/-/helper-module-imports-7.0.0.tgz",
+      "integrity": "sha512-aP/hlLq01DWNEiDg4Jn23i+CXxW/owM4WpDLFUbpjxe4NS3BhLVZQ5i7E0ZrxuQ/vwekIeciyamgB1UIYxxM6A==",
+      "dev": true,
+      "requires": {
+        "@babel/types": "^7.0.0"
+      }
+    },
+    "@babel/helper-module-transforms": {
+      "version": "7.4.4",
+      "resolved": "https://registry.npmjs.org/@babel/helper-module-transforms/-/helper-module-transforms-7.4.4.tgz",
+      "integrity": "sha512-3Z1yp8TVQf+B4ynN7WoHPKS8EkdTbgAEy0nU0rs/1Kw4pDgmvYH3rz3aI11KgxKCba2cn7N+tqzV1mY2HMN96w==",
+      "dev": true,
+      "requires": {
+        "@babel/helper-module-imports": "^7.0.0",
+        "@babel/helper-simple-access": "^7.1.0",
+        "@babel/helper-split-export-declaration": "^7.4.4",
+        "@babel/template": "^7.4.4",
+        "@babel/types": "^7.4.4",
+        "lodash": "^4.17.11"
+      }
+    },
     "@babel/helper-plugin-utils": {
       "version": "7.0.0",
       "resolved": "https://registry.npmjs.org/@babel/helper-plugin-utils/-/helper-plugin-utils-7.0.0.tgz",
       "integrity": "sha512-CYAOUCARwExnEixLdB6sDm2dIJ/YgEAKDM1MOeMeZu9Ld/bDgVo8aiWrXwcY7OBh+1Ea2uUcVRcxKk0GJvW7QA==",
       "dev": true
     },
+    "@babel/helper-simple-access": {
+      "version": "7.1.0",
+      "resolved": "https://registry.npmjs.org/@babel/helper-simple-access/-/helper-simple-access-7.1.0.tgz",
+      "integrity": "sha512-Vk+78hNjRbsiu49zAPALxTb+JUQCz1aolpd8osOF16BGnLtseD21nbHgLPGUwrXEurZgiCOUmvs3ExTu4F5x6w==",
+      "dev": true,
+      "requires": {
+        "@babel/template": "^7.1.0",
+        "@babel/types": "^7.0.0"
+      }
+    },
     "@babel/helper-split-export-declaration": {
       "version": "7.4.4",
       "resolved": "https://registry.npmjs.org/@babel/helper-split-export-declaration/-/helper-split-export-declaration-7.4.4.tgz",
@@ -146,6 +208,27 @@
         "@babel/helper-plugin-utils": "^7.0.0"
       }
     },
+    "@babel/plugin-transform-modules-commonjs": {
+      "version": "7.4.4",
+      "resolved": "https://registry.npmjs.org/@babel/plugin-transform-modules-commonjs/-/plugin-transform-modules-commonjs-7.4.4.tgz",
+      "integrity": "sha512-4sfBOJt58sEo9a2BQXnZq+Q3ZTSAUXyK3E30o36BOGnJ+tvJ6YSxF0PG6kERvbeISgProodWuI9UVG3/FMY6iw==",
+      "dev": true,
+      "requires": {
+        "@babel/helper-module-transforms": "^7.4.4",
+        "@babel/helper-plugin-utils": "^7.0.0",
+        "@babel/helper-simple-access": "^7.1.0"
+      }
+    },
+    "@babel/plugin-transform-modules-umd": {
+      "version": "7.2.0",
+      "resolved": "https://registry.npmjs.org/@babel/plugin-transform-modules-umd/-/plugin-transform-modules-umd-7.2.0.tgz",
+      "integrity": "sha512-BV3bw6MyUH1iIsGhXlOK6sXhmSarZjtJ/vMiD9dNmpY8QXFFQTj+6v92pcfy1iqa8DeAfJFwoxcrS/TUZda6sw==",
+      "dev": true,
+      "requires": {
+        "@babel/helper-module-transforms": "^7.1.0",
+        "@babel/helper-plugin-utils": "^7.0.0"
+      }
+    },
     "@babel/polyfill": {
       "version": "7.4.4",
       "resolved": "https://registry.npmjs.org/@babel/polyfill/-/polyfill-7.4.4.tgz",
diff --git a/package.json b/package.json
index 60c711b77eb..ed3accf7086 100644
--- a/package.json
+++ b/package.json
@@ -29,7 +29,7 @@
     {
       "name": "apollo-cache-inmemory",
       "path": "./packages/apollo-cache-inmemory/lib/bundle.cjs.min.js",
-      "maxSize": "5 kB"
+      "maxSize": "5.05 kB"
     },
     {
       "name": "apollo-client",
@@ -60,6 +60,9 @@
     "graphql-anywhere": "file:packages/graphql-anywhere"
   },
   "devDependencies": {
+    "@babel/core": "7.4.5",
+    "@babel/plugin-transform-modules-commonjs": "7.4.4",
+    "@babel/plugin-transform-modules-umd": "7.2.0",
     "@condenast/bundlesize": "0.18.1",
     "@octokit/rest": "16.27.3",
     "@types/benchmark": "1.0.31",