diff --git a/packages/block-editor/src/components/inserter/menu.js b/packages/block-editor/src/components/inserter/menu.js
index 4f028eb69c6662..cd44b902f491a5 100644
--- a/packages/block-editor/src/components/inserter/menu.js
+++ b/packages/block-editor/src/components/inserter/menu.js
@@ -191,17 +191,13 @@ function InserterMenu(
 		]
 	);
 
-	const getCurrentTab = useCallback(
-		( tab ) => {
-			if ( tab.name === 'blocks' ) {
-				return blocksTab;
-			} else if ( tab.name === 'patterns' ) {
-				return patternsTab;
-			} else if ( tab.name === 'media' ) {
-				return mediaTab;
-			}
-		},
-		[ blocksTab, patternsTab, mediaTab ]
+	const inserterTabsContents = useMemo(
+		() => ( {
+			blocks: blocksTab,
+			patterns: patternsTab,
+			media: mediaTab,
+		} ),
+		[ blocksTab, mediaTab, patternsTab ]
 	);
 
 	const searchRef = useRef();
@@ -275,9 +271,8 @@ function InserterMenu(
 						showMedia={ showMedia }
 						prioritizePatterns={ prioritizePatterns }
 						onSelect={ handleSetSelectedTab }
-					>
-						{ getCurrentTab }
-					</InserterTabs>
+						tabsContents={ inserterTabsContents }
+					/>
 				) }
 				{ ! delayedFilterValue && ! showAsTabs && (
 					<div className="block-editor-inserter__no-tab-container">
diff --git a/packages/block-editor/src/components/inserter/style.scss b/packages/block-editor/src/components/inserter/style.scss
index 755445246e8596..97a3d877b7e72a 100644
--- a/packages/block-editor/src/components/inserter/style.scss
+++ b/packages/block-editor/src/components/inserter/style.scss
@@ -61,7 +61,7 @@ $block-inserter-tabs-height: 44px;
 .block-editor-inserter__popover .block-editor-inserter__menu {
 	margin: -$grid-unit-15;
 
-	.block-editor-inserter__tabs .components-tab-panel__tabs {
+	.block-editor-inserter__tabs div[role="tablist"] {
 		top: $grid-unit-10 + $grid-unit-20 + $grid-unit-60 - $grid-unit-15;
 	}
 
@@ -118,10 +118,10 @@ $block-inserter-tabs-height: 44px;
 	flex-direction: column;
 	overflow: hidden;
 
-	.components-tab-panel__tabs {
+	div[role="tablist"] {
 		border-bottom: $border-width solid $gray-300;
 
-		.components-tab-panel__tabs-item {
+		button[role="tab"] {
 			flex-grow: 1;
 			margin-bottom: -$border-width;
 			&[id$="reusable"] {
@@ -133,7 +133,7 @@ $block-inserter-tabs-height: 44px;
 		}
 	}
 
-	.components-tab-panel__tab-content {
+	div[role="tabpanel"] {
 		display: flex;
 		flex-grow: 1;
 		flex-direction: column;
diff --git a/packages/block-editor/src/components/inserter/tabs.js b/packages/block-editor/src/components/inserter/tabs.js
index a75e0029ef4900..72b13425bbbe79 100644
--- a/packages/block-editor/src/components/inserter/tabs.js
+++ b/packages/block-editor/src/components/inserter/tabs.js
@@ -2,9 +2,16 @@
  * WordPress dependencies
  */
 import { useMemo } from '@wordpress/element';
-import { TabPanel } from '@wordpress/components';
+import { privateApis as componentsPrivateApis } from '@wordpress/components';
 import { __ } from '@wordpress/i18n';
 
+/**
+ * Internal dependencies
+ */
+import { unlock } from '../../lock-unlock';
+
+const { Tabs } = unlock( componentsPrivateApis );
+
 const blocksTab = {
 	name: 'blocks',
 	/* translators: Blocks tab title in the block inserter. */
@@ -23,11 +30,11 @@ const mediaTab = {
 };
 
 function InserterTabs( {
-	children,
 	showPatterns = false,
 	showMedia = false,
 	onSelect,
 	prioritizePatterns,
+	tabsContents,
 } ) {
 	const tabs = useMemo( () => {
 		const tempTabs = [];
@@ -45,13 +52,26 @@ function InserterTabs( {
 	}, [ prioritizePatterns, showPatterns, showMedia ] );
 
 	return (
-		<TabPanel
-			className="block-editor-inserter__tabs"
-			tabs={ tabs }
-			onSelect={ onSelect }
-		>
-			{ children }
-		</TabPanel>
+		<div className="block-editor-inserter__tabs">
+			<Tabs onSelect={ onSelect }>
+				<Tabs.TabList>
+					{ tabs.map( ( tab ) => (
+						<Tabs.Tab key={ tab.name } tabId={ tab.name }>
+							{ tab.title }
+						</Tabs.Tab>
+					) ) }
+				</Tabs.TabList>
+				{ tabs.map( ( tab ) => (
+					<Tabs.TabPanel
+						key={ tab.name }
+						tabId={ tab.name }
+						focusable={ false }
+					>
+						{ tabsContents[ tab.name ] }
+					</Tabs.TabPanel>
+				) ) }
+			</Tabs>
+		</div>
 	);
 }
 
diff --git a/packages/e2e-test-utils/src/inserter.js b/packages/e2e-test-utils/src/inserter.js
index ebbda244d18564..a2c73abe666552 100644
--- a/packages/e2e-test-utils/src/inserter.js
+++ b/packages/e2e-test-utils/src/inserter.js
@@ -86,7 +86,10 @@ export async function selectGlobalInserterTab( label ) {
 	}
 
 	const activeTab = await page.waitForSelector(
-		'.block-editor-inserter__tabs button.is-active'
+		// Targeting a class name is necessary here, because there are likely
+		// two implementations of the `Tabs` component visible to this test, and
+		// we want to confirm that it's waiting for the correct one.
+		'.block-editor-inserter__tabs [role="tab"][aria-selected="true"]'
 	);
 
 	const activeTabLabel = await page.evaluate(