diff --git a/src/vaadin-grid.html b/src/vaadin-grid.html
index 96d76efd6..bfbac1e0e 100644
--- a/src/vaadin-grid.html
+++ b/src/vaadin-grid.html
@@ -342,6 +342,12 @@
 
       static get properties() {
         return {
+          /** @private */
+          _chrome: {
+            type: Boolean,
+            value: /Chrome/.test(navigator.userAgent) && /Google Inc/.test(navigator.vendor)
+          },
+
           /** @private */
           _safari: {
             type: Boolean,
@@ -607,13 +613,16 @@
         // focusable slot wrapper, that is why cells are not focused with
         // mousedown. Workaround: listen for mousedown and focus manually.
         cellContent.addEventListener('mousedown', () => {
-          if (window.chrome) {
+          if (this._chrome) {
             // Chrome bug: focusing before mouseup prevents text selection, see http://crbug.com/771903
-            const mouseUpListener = () => {
-              if (!cellContent.contains(this.getRootNode().activeElement)) {
+            const mouseUpListener = (event) => {
+              // If focus is on element within the cell content — respect it, do not change
+              const contentContainsFocusedElement = cellContent.contains(this.getRootNode().activeElement);
+              // Only focus if mouse is released on cell content itself
+              const mouseUpWithinCell = event.composedPath().indexOf(cellContent) >= 0;
+              if (!contentContainsFocusedElement && mouseUpWithinCell) {
                 cell.focus();
               }
-              // If focus is in the cell content — respect it, do not change.
               document.removeEventListener('mouseup', mouseUpListener, true);
             };
             document.addEventListener('mouseup', mouseUpListener, true);
diff --git a/test/keyboard-navigation.html b/test/keyboard-navigation.html
index 383697a02..230665cc1 100644
--- a/test/keyboard-navigation.html
+++ b/test/keyboard-navigation.html
@@ -230,6 +230,16 @@
       MockInteractions.keyDownOn(target || grid.shadowRoot.activeElement, 113, [], 'F2');
     }
 
+    function mouseDown(target) {
+      const event = new CustomEvent('mousedown', {bubbles: true, cancelable: true, composed: true});
+      target.dispatchEvent(event);
+    }
+
+    function mouseUp(target) {
+      const event = new CustomEvent('mouseup', {bubbles: true, cancelable: true, composed: true});
+      target.dispatchEvent(event);
+    }
+
     function getFirstHeaderCell() {
       return grid.$.header.children[0].children[0];
     }
@@ -1914,6 +1924,63 @@
 
           expect(spy.calledOnce).to.be.true;
         });
+
+        // Separate test suite for Chrome, where we use a workaround to dispatch
+        // cell-focus on mouse up
+        const isChrome = /Chrome/.test(navigator.userAgent) && /Google Inc/.test(navigator.vendor);
+        (isChrome ? describe : describe.skip)('chrome', () => {
+          it('should dispatch cell-focus on mouse up on cell content', () => {
+            const spy = sinon.spy();
+            grid.addEventListener('cell-focus', spy);
+
+            // Mouse down and release on cell content element
+            const cell = getRowFirstCell(0);
+            mouseDown(cell._content);
+            mouseUp(cell._content);
+            expect(spy.calledOnce).to.be.true;
+          });
+
+          it('should dispatch cell-focus on mouse up on cell content, when grid is in shadow DOM', () => {
+            const spy = sinon.spy();
+            grid.addEventListener('cell-focus', spy);
+
+            // Move grid into a shadow DOM
+            const container = document.createElement('div');
+            document.body.appendChild(container);
+            container.attachShadow({mode: 'open'});
+            container.shadowRoot.appendChild(grid);
+
+            // Mouse down and release on cell content element
+            const cell = getRowFirstCell(0);
+            mouseDown(cell._content);
+            mouseUp(cell._content);
+            expect(spy.calledOnce).to.be.true;
+          });
+
+          it('should dispatch cell-focus on mouse up within cell content', () => {
+            const spy = sinon.spy();
+            grid.addEventListener('cell-focus', spy);
+
+            // Mouse down and release on cell content child
+            const cell = getRowFirstCell(0);
+            const contentSpan = document.createElement('span');
+            cell._content.appendChild(contentSpan);
+
+            mouseDown(contentSpan);
+            mouseUp(contentSpan);
+            expect(spy.calledOnce).to.be.true;
+          });
+
+          // Regression test for https://github.com/vaadin/flow-components/issues/2863
+          it('should not dispatch cell-focus on mouse up outside of cell', () => {
+            const spy = sinon.spy();
+            grid.addEventListener('cell-focus', spy);
+
+            mouseDown(getRowFirstCell(0)._content);
+            mouseUp(document.body);
+            expect(spy.calledOnce).to.be.false;
+          });
+        });
       });
     });