diff --git a/lib/internal/webstreams/adapters.js b/lib/internal/webstreams/adapters.js
index 6c2be59a24a72a..4db8e0ab28b83e 100644
--- a/lib/internal/webstreams/adapters.js
+++ b/lib/internal/webstreams/adapters.js
@@ -67,6 +67,7 @@ const {
   createDeferredPromise,
   kEmptyObject,
   normalizeEncoding,
+  once,
 } = require('internal/util');
 
 const {
@@ -471,7 +472,7 @@ function newReadableStreamFromStreamReadable(streamReadable, options = kEmptyObj
 
   streamReadable.pause();
 
-  const cleanup = finished(streamReadable, (error) => {
+  const onFinished = once((error) => {
     error = handleKnownInternalErrors(error);
 
     cleanup();
@@ -482,6 +483,7 @@ function newReadableStreamFromStreamReadable(streamReadable, options = kEmptyObj
       return controller.error(error);
     controller.close();
   });
+  const cleanup = finished(streamReadable, onFinished);
 
   streamReadable.on('data', onData);
 
@@ -491,7 +493,9 @@ function newReadableStreamFromStreamReadable(streamReadable, options = kEmptyObj
     pull() { streamReadable.resume(); },
 
     cancel(reason) {
-      destroy(streamReadable, reason);
+      const error = reason || new ERR_STREAM_PREMATURE_CLOSE();
+      onFinished(error);
+      destroy(streamReadable, error);
     },
   }, strategy);
 }
diff --git a/test/parallel/test-stream-readable-from-web-termination.js b/test/parallel/test-stream-readable-from-web-termination.js
new file mode 100644
index 00000000000000..68ed7d69694089
--- /dev/null
+++ b/test/parallel/test-stream-readable-from-web-termination.js
@@ -0,0 +1,15 @@
+'use strict';
+require('../common');
+const { Readable } = require('stream');
+
+{
+  const r = Readable.from(['data']);
+
+  const wrapper = Readable.fromWeb(Readable.toWeb(r));
+
+  wrapper.on('data', () => {
+    // Destroying wrapper while emitting data should not cause uncaught
+    // exceptions
+    wrapper.destroy();
+  });
+}
diff --git a/test/parallel/test-stream-readable-to-web-termination.js b/test/parallel/test-stream-readable-to-web-termination.js
new file mode 100644
index 00000000000000..13fce9bc715e1e
--- /dev/null
+++ b/test/parallel/test-stream-readable-to-web-termination.js
@@ -0,0 +1,12 @@
+'use strict';
+require('../common');
+const { Readable } = require('stream');
+
+{
+  const r = Readable.from([]);
+  // Cancelling reader while closing should not cause uncaught exceptions
+  r.on('close', () => reader.cancel());
+
+  const reader = Readable.toWeb(r).getReader();
+  reader.read();
+}