diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8978feb20ec..4959b77e78d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@
 **Bug fixes**
 
 - Fixed inconsistent width of `EuiRange` and `EuiDualRange` with custom tick values ([#4781](https://github.com/elastic/eui/pull/4781))
+- Fixes browser freezing when `EuiDataGrid` is used together with `EuiFlyout` and the user clicks a cell ([4813](https://github.com/elastic/eui/pull/4813))
 
 ## [`34.0.0`](https://github.com/elastic/eui/tree/v34.0.0)
 
diff --git a/src/components/datagrid/data_grid.test.tsx b/src/components/datagrid/data_grid.test.tsx
index 36571f64abb..13fcbd5f825 100644
--- a/src/components/datagrid/data_grid.test.tsx
+++ b/src/components/datagrid/data_grid.test.tsx
@@ -2300,7 +2300,7 @@ describe('EuiDataGrid', () => {
       ).toEqual('6, C');
     });
 
-    it('does not break arrow key focus control behavior when also using a mouse', () => {
+    it('does not break arrow key focus control behavior when also using a mouse', async () => {
       const component = mount(
         <EuiDataGrid
           {...requiredProps}
@@ -2334,6 +2334,12 @@ describe('EuiDataGrid', () => {
 
       findTestSubject(component, 'dataGridRowCell').at(3).simulate('focus');
 
+      // wait for a tick to give focus logic time to run
+      await act(async () => {
+        await new Promise((r) => setTimeout(r, 0));
+      });
+      component.update();
+
       focusableCell = getFocusableCell(component);
       expect(focusableCell.length).toEqual(1);
       expect(
diff --git a/src/components/datagrid/data_grid_cell.tsx b/src/components/datagrid/data_grid_cell.tsx
index 9ad88f45ab4..a936eb495e7 100644
--- a/src/components/datagrid/data_grid_cell.tsx
+++ b/src/components/datagrid/data_grid_cell.tsx
@@ -152,6 +152,7 @@ export class EuiDataGridCell extends Component<
     disableCellTabIndex: false,
   };
   unsubscribeCell?: Function = () => {};
+  focusTimeout: number | undefined;
   style = null;
 
   setCellRef = (ref: HTMLDivElement | null) => {
@@ -227,6 +228,7 @@ export class EuiDataGridCell extends Component<
   };
 
   componentWillUnmount() {
+    window.clearTimeout(this.focusTimeout);
     if (this.unsubscribeCell) {
       this.unsubscribeCell();
     }
@@ -286,13 +288,16 @@ export class EuiDataGridCell extends Component<
     //      event up, which can trigger the focus() call below, causing focus lock fighting
     if (this.cellRef.current === e.target) {
       const { colIndex, visibleRowIndex, isExpandable } = this.props;
-      this.context.setFocusedCell([colIndex, visibleRowIndex]);
+      // focus in next tick to give potential focus capturing mechanisms time to release their traps
+      this.focusTimeout = window.setTimeout(() => {
+        this.context.setFocusedCell([colIndex, visibleRowIndex]);
 
-      const interactables = this.getInteractables();
-      if (interactables.length === 1 && isExpandable === false) {
-        interactables[0].focus();
-        this.setState({ disableCellTabIndex: true });
-      }
+        const interactables = this.getInteractables();
+        if (interactables.length === 1 && isExpandable === false) {
+          interactables[0].focus();
+          this.setState({ disableCellTabIndex: true });
+        }
+      }, 0);
     }
   };
 
diff --git a/src/components/popover/popover.tsx b/src/components/popover/popover.tsx
index c741b09523c..fe890e49e40 100644
--- a/src/components/popover/popover.tsx
+++ b/src/components/popover/popover.tsx
@@ -472,6 +472,9 @@ export class EuiPopover extends Component<Props, State> {
 
   onOpenPopover = () => {
     clearTimeout(this.closingTransitionTimeout);
+    if (this.closingTransitionAnimationFrame) {
+      cancelAnimationFrame(this.closingTransitionAnimationFrame);
+    }
     // We need to set this state a beat after the render takes place, so that the CSS
     // transition can take effect.
     this.closingTransitionAnimationFrame = window.requestAnimationFrame(() => {
@@ -498,6 +501,7 @@ export class EuiPopover extends Component<Props, State> {
         { durationMatch: 0, delayMatch: 0 }
       );
 
+    clearTimeout(this.respositionTimeout);
     this.respositionTimeout = window.setTimeout(() => {
       this.setState({ isOpenStable: true }, () => {
         this.positionPopoverFixed();