diff --git a/packages/devextreme/js/__internal/ui/overlay/overlay.ts b/packages/devextreme/js/__internal/ui/overlay/overlay.ts
index 3c421693ef7d..c1a9e9123a2f 100644
--- a/packages/devextreme/js/__internal/ui/overlay/overlay.ts
+++ b/packages/devextreme/js/__internal/ui/overlay/overlay.ts
@@ -565,14 +565,13 @@ class Overlay<
     super._initTemplates();
   }
 
-  _isTopOverlay(): boolean {
+  _isTopFocusableOverlay(): boolean {
     const overlayStack = this._overlayStack();
 
     for (let i = overlayStack.length - 1; i >= 0; i -= 1) {
       const tabbableElements = overlayStack[i]._findTabbableBounds();
 
       if (tabbableElements.$first || tabbableElements.$last) {
-        // @ts-ignore expected: types Overlay<OverlayProperties> and this have no overlap
         return overlayStack[i] === this;
       }
     }
@@ -580,6 +579,25 @@ class Overlay<
     return false;
   }
 
+  _isLastInOverlayStack(): boolean {
+    const overlayStack = this._overlayStack();
+
+    return overlayStack[overlayStack.length - 1] === this;
+  }
+
+  _handlesDocumentEscapeKey(): boolean {
+    return false;
+  }
+
+  _isEscapeHandledByOverlayAbove(): boolean {
+    const overlayStack = this._overlayStack();
+    const index = overlayStack.indexOf(this);
+
+    return overlayStack
+      .slice(index + 1)
+      .some((overlay) => overlay._handlesDocumentEscapeKey());
+  }
+
   // eslint-disable-next-line @typescript-eslint/no-explicit-any
   _overlayStack(): Overlay<any>[] {
     return OVERLAY_STACK;
@@ -1045,7 +1063,7 @@ class Overlay<
   }
 
   _tabKeyHandler(e: KeyboardEvent): void {
-    if (normalizeKeyName(e) !== TAB_KEY || !this._isTopOverlay()) {
+    if (normalizeKeyName(e) !== TAB_KEY || !this._isTopFocusableOverlay()) {
       return;
     }
 
diff --git a/packages/devextreme/js/__internal/ui/popover/popover.ts b/packages/devextreme/js/__internal/ui/popover/popover.ts
index fd035ad9ba86..ccd6279eba83 100644
--- a/packages/devextreme/js/__internal/ui/popover/popover.ts
+++ b/packages/devextreme/js/__internal/ui/popover/popover.ts
@@ -215,18 +215,19 @@ class Popover<
 
   _initEscapeKeyHandler(): void {
     this._documentEscapeKeyHandler = (e: KeyboardEvent): void => {
-      const { visible } = this.option();
-
-      const overlayStack = this._overlayStack();
-      const isTopOverlay = overlayStack[overlayStack.length - 1] === this;
-
-      if (normalizeKeyName(e) === ESC_KEY_NAME && visible && isTopOverlay) {
+      if (normalizeKeyName(e) === ESC_KEY_NAME && this._handlesDocumentEscapeKey()) {
         // eslint-disable-next-line @typescript-eslint/no-floating-promises
         this.hide();
       }
     };
   }
 
+  _handlesDocumentEscapeKey(): boolean {
+    const { visible } = this.option();
+
+    return Boolean(visible) && this._isLastInOverlayStack();
+  }
+
   _attachEscapeKeyHandler(): void {
     const eventName = addNamespace('keydown', this.NAME as string);
 
diff --git a/packages/devextreme/js/__internal/ui/popup/popup.ts b/packages/devextreme/js/__internal/ui/popup/popup.ts
index 0c67ef664cd9..ea0276e5b231 100644
--- a/packages/devextreme/js/__internal/ui/popup/popup.ts
+++ b/packages/devextreme/js/__internal/ui/popup/popup.ts
@@ -246,10 +246,14 @@ class Popup<
     const e = options.originalEvent;
     const $target = $(e.target);
 
-    if (this._$content && !$target.is(this._$content)
-        && options.keyName === ESC_KEY_NAME
-        && !e.isDefaultPrevented()
-        && !_ignoreCloseOnChildEscape) {
+    const shouldCloseOnChildEscape = !!this._$content
+      && !$target.is(this._$content)
+      && options.keyName === ESC_KEY_NAME
+      && !e.isDefaultPrevented()
+      && !_ignoreCloseOnChildEscape
+      && !this._isEscapeHandledByOverlayAbove();
+
+    if (shouldCloseOnChildEscape) {
       // eslint-disable-next-line @typescript-eslint/no-floating-promises
       this.hide();
     }
diff --git a/packages/devextreme/testing/tests/DevExpress.ui.widgets/popup.tests.js b/packages/devextreme/testing/tests/DevExpress.ui.widgets/popup.tests.js
index 468828b4ea61..c4b9ce3c76a2 100644
--- a/packages/devextreme/testing/tests/DevExpress.ui.widgets/popup.tests.js
+++ b/packages/devextreme/testing/tests/DevExpress.ui.widgets/popup.tests.js
@@ -33,6 +33,8 @@ import { BUTTON_CLASS } from '__internal/ui/button/button';
 
 import 'fluent_blue_light.css!';
 import 'ui/popup';
+import 'ui/tooltip';
+import 'ui/load_panel';
 import 'ui/tab_panel';
 import 'ui/scroll_view';
 import 'ui/date_box';
@@ -2725,6 +2727,41 @@ QUnit.module('keyboard navigation', {
 
         assert.strictEqual(this.popup.option('visible'), true, 'popup remains visible when _ignoreCloseOnChildEscape is true');
     });
+
+    QUnit.test('should remain visible when child element presses escape and a tooltip is shown above it (T1334708)', function(assert) {
+        this.init({ dragEnabled: false });
+
+        const $input = $('<input>').appendTo(this.popup.$content());
+        const tooltip = $('<div>')
+            .appendTo('#qunit-fixture')
+            .dxTooltip({ target: $input, visible: true, animation: null })
+            .dxTooltip('instance');
+
+        assert.strictEqual(tooltip.option('visible'), true, 'tooltip is shown');
+
+        keyboardMock($input).keyDown('esc');
+
+        assert.strictEqual(tooltip.option('visible'), false, 'tooltip is hidden');
+        assert.strictEqual(this.popup.option('visible'), true, 'popup remains visible');
+
+        tooltip.dispose();
+    });
+
+    QUnit.test('should be closed on child element escape key press when an overlay that ignores escape is shown above it', function(assert) {
+        this.init({ dragEnabled: false });
+
+        const $input = $('<input>').appendTo(this.popup.$content());
+        const loadPanel = $('<div>')
+            .appendTo('#qunit-fixture')
+            .dxLoadPanel({ visible: true, animation: null })
+            .dxLoadPanel('instance');
+
+        keyboardMock($input).keyDown('esc');
+
+        assert.strictEqual(this.popup.option('visible'), false, 'popup is closed');
+
+        loadPanel.dispose();
+    });
 });
 
 QUnit.module('rendering', {