diff --git a/packages/material-ui/src/Tooltip/Tooltip.js b/packages/material-ui/src/Tooltip/Tooltip.js
index 7f4feb1a966b54..5cbf56f444d280 100644
--- a/packages/material-ui/src/Tooltip/Tooltip.js
+++ b/packages/material-ui/src/Tooltip/Tooltip.js
@@ -150,6 +150,14 @@ export const styles = theme => ({
   },
 });
 
+let hystersisOpen = false;
+let hystersisTimer = null;
+
+export function testReset() {
+  hystersisOpen = false;
+  clearTimeout(hystersisTimer);
+}
+
 const Tooltip = React.forwardRef(function Tooltip(props, ref) {
   const {
     arrow = false,
@@ -160,7 +168,7 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
     disableTouchListener = false,
     enterDelay = 0,
     enterTouchDelay = 700,
-    id,
+    id: idProp,
     interactive = false,
     leaveDelay = 0,
     leaveTouchDelay = 1500,
@@ -176,11 +184,10 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
   } = props;
   const theme = useTheme();
 
-  const [, forceUpdate] = React.useState(0);
   const [childNode, setChildNode] = React.useState();
   const [arrowRef, setArrowRef] = React.useState(null);
   const ignoreNonTouchEvents = React.useRef(false);
-  const defaultId = React.useRef();
+
   const closeTimer = React.useRef();
   const enterTimer = React.useRef();
   const leaveTimer = React.useRef();
@@ -232,19 +239,18 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
     }, [isControlled, title, childNode]);
   }
 
+  const [defaultId, setDefaultId] = React.useState();
+  const id = idProp || defaultId;
   React.useEffect(() => {
+    if (!open || defaultId) {
+      return;
+    }
+
     // Fallback to this default id when possible.
     // Use the random value for client-side rendering only.
     // We can't use it server-side.
-    if (!defaultId.current) {
-      defaultId.current = `mui-tooltip-${Math.round(Math.random() * 1e5)}`;
-    }
-
-    // Rerender with defaultId and childNode.
-    if (openProp) {
-      forceUpdate(n => !n);
-    }
-  }, [openProp]);
+    setDefaultId(`mui-tooltip-${Math.round(Math.random() * 1e5)}`);
+  }, [open, defaultId]);
 
   React.useEffect(() => {
     return () => {
@@ -256,6 +262,9 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
   }, []);
 
   const handleOpen = event => {
+    clearTimeout(hystersisTimer);
+    hystersisOpen = true;
+
     // The mouseover event will trigger for every nested element in the tooltip.
     // We can skip rerendering when the tooltip is already open.
     // We are using the mouseover event instead of the mouseenter event to fix a hide/show issue.
@@ -288,7 +297,7 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
 
     clearTimeout(enterTimer.current);
     clearTimeout(leaveTimer.current);
-    if (enterDelay) {
+    if (enterDelay && !hystersisOpen) {
       event.persist();
       enterTimer.current = setTimeout(() => {
         handleOpen(event);
@@ -327,6 +336,12 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
   };
 
   const handleClose = event => {
+    clearTimeout(hystersisTimer);
+    hystersisTimer = setTimeout(() => {
+      hystersisOpen = false;
+    }, 500);
+    // Use 500 ms per https://github.com/reach/reach-ui/blob/3b5319027d763a3082880be887d7a29aee7d3afc/packages/tooltip/src/index.js#L214
+
     if (!isControlled) {
       setOpenState(false);
     }
@@ -417,7 +432,7 @@ const Tooltip = React.forwardRef(function Tooltip(props, ref) {
   // We are open to change the tradeoff.
   const shouldShowNativeTitle = !open && !disableHoverListener;
   const childrenProps = {
-    'aria-describedby': open ? id || defaultId.current : null,
+    'aria-describedby': open ? id : null,
     title: shouldShowNativeTitle && typeof title === 'string' ? title : null,
     ...other,
     ...children.props,
diff --git a/packages/material-ui/src/Tooltip/Tooltip.test.js b/packages/material-ui/src/Tooltip/Tooltip.test.js
index fa22cf9bb5a550..870e1ac9d699ea 100644
--- a/packages/material-ui/src/Tooltip/Tooltip.test.js
+++ b/packages/material-ui/src/Tooltip/Tooltip.test.js
@@ -4,19 +4,25 @@ import PropTypes from 'prop-types';
 import { spy, useFakeTimers } from 'sinon';
 import consoleErrorMock from 'test/utils/consoleErrorMock';
 import { createMount, getClasses } from '@material-ui/core/test-utils';
+import { act, createClientRender, fireEvent } from 'test/utils/createClientRender';
 import describeConformance from '../test-utils/describeConformance';
 import Popper from '../Popper';
-import Tooltip from './Tooltip';
+import Tooltip, { testReset } from './Tooltip';
 import Input from '../Input';
-import createMuiTheme from '../styles/createMuiTheme';
 
-const theme = createMuiTheme();
-
-function focusVisible(wrapper) {
+function focusVisibleLegacy(wrapper) {
   document.dispatchEvent(new window.Event('keydown'));
   wrapper.simulate('focus');
 }
 
+function focusVisible(element) {
+  act(() => {
+    element.blur();
+    fireEvent.keyDown(document.activeElement || document.body, { key: 'Tab' });
+    element.focus();
+  });
+}
+
 function simulatePointerDevice() {
   // first focus on a page triggers focus visible until a pointer event
   // has been dispatched
@@ -26,30 +32,38 @@ function simulatePointerDevice() {
 describe('<Tooltip />', () => {
   let mount;
   let classes;
+  const render = createClientRender({ strict: false });
   let clock;
   const defaultProps = {
-    children: <span id="testChild">Hello World</span>,
-    theme,
+    children: (
+      <button id="testChild" type="submit">
+        Hello World
+      </button>
+    ),
     title: 'Hello World',
   };
 
   before(() => {
-    // StrictModeViolation: uses Grow and tests a lot of impl details
-    mount = createMount({ strict: undefined });
     classes = getClasses(<Tooltip {...defaultProps} />);
+  });
+
+  beforeEach(() => {
+    testReset();
     clock = useFakeTimers();
+    // StrictModeViolation: uses Grow and tests a lot of impl details
+    mount = createMount({ strict: undefined });
   });
 
-  after(() => {
+  afterEach(() => {
     clock.restore();
     mount.cleanUp();
   });
 
   describeConformance(<Tooltip {...defaultProps} />, () => ({
     classes,
-    inheritComponent: 'span',
+    inheritComponent: 'button',
     mount,
-    refInstanceof: window.HTMLSpanElement,
+    refInstanceof: window.HTMLButtonElement,
     skip: [
       'componentProp',
       // react-transition-group issue
@@ -117,7 +131,6 @@ describe('<Tooltip />', () => {
     clock.tick(0);
     wrapper.update();
     assert.strictEqual(wrapper.find(Popper).props().open, false);
-    assert.strictEqual(wrapper.find(Popper).props().open, false);
   });
 
   it('should be controllable', () => {
@@ -193,16 +206,40 @@ describe('<Tooltip />', () => {
 
   describe('prop: delay', () => {
     it('should take the enterDelay into account', () => {
-      const wrapper = mount(<Tooltip enterDelay={111} {...defaultProps} />);
+      const wrapper = mount(<Tooltip {...defaultProps} enterDelay={111} />);
       simulatePointerDevice();
       const children = wrapper.find('#testChild');
-      focusVisible(children);
+      focusVisibleLegacy(children);
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), false);
       clock.tick(111);
       wrapper.update();
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), true);
     });
 
+    it('should use hysteresis with the enterDelay', () => {
+      const { container } = render(
+        <Tooltip
+          enterDelay={111}
+          leaveDelay={5}
+          TransitionProps={{ timeout: 6 }}
+          {...defaultProps}
+        />,
+      );
+      const children = container.querySelector('#testChild');
+      focusVisible(children);
+      assert.strictEqual(document.body.querySelectorAll('[role="tooltip"]').length, 0);
+      clock.tick(111);
+      assert.strictEqual(document.body.querySelectorAll('[role="tooltip"]').length, 1);
+      document.activeElement.blur();
+      clock.tick(5);
+      clock.tick(6);
+      assert.strictEqual(document.body.querySelectorAll('[role="tooltip"]').length, 0);
+
+      focusVisible(children);
+      // Bypass `enterDelay` wait, instant display.
+      assert.strictEqual(document.body.querySelectorAll('[role="tooltip"]').length, 1);
+    });
+
     it('should take the leaveDelay into account', () => {
       const childRef = React.createRef();
       const wrapper = mount(
@@ -212,7 +249,7 @@ describe('<Tooltip />', () => {
       );
       simulatePointerDevice();
       const children = wrapper.find('#testChild');
-      focusVisible(children);
+      focusVisibleLegacy(children);
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), true);
       children.simulate('blur');
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), true);
@@ -345,7 +382,7 @@ describe('<Tooltip />', () => {
   describe('forward', () => {
     it('should forward props to the child element', () => {
       const wrapper = mount(
-        <Tooltip className="foo" {...defaultProps}>
+        <Tooltip {...defaultProps} className="foo">
           <h1 className="bar">H1</h1>
         </Tooltip>,
       );
@@ -354,7 +391,7 @@ describe('<Tooltip />', () => {
 
     it('should respect the props priority', () => {
       const wrapper = mount(
-        <Tooltip hidden {...defaultProps}>
+        <Tooltip {...defaultProps} hidden>
           <h1 hidden={false}>H1</h1>
         </Tooltip>,
       );
@@ -390,7 +427,7 @@ describe('<Tooltip />', () => {
 
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), false);
 
-      focusVisible(wrapper.find('#target'));
+      focusVisibleLegacy(wrapper.find('#target'));
 
       assert.strictEqual(wrapper.find('[role="tooltip"]').exists(), true);
     });