diff --git a/packages/editor/src/components/post-template/block-theme.js b/packages/editor/src/components/post-template/block-theme.js
index 62de10a2c715ff..6d7f7f787b32f8 100644
--- a/packages/editor/src/components/post-template/block-theme.js
+++ b/packages/editor/src/components/post-template/block-theme.js
@@ -4,12 +4,18 @@
 import { useSelect, useDispatch } from '@wordpress/data';
 import { decodeEntities } from '@wordpress/html-entities';
 import { DropdownMenu, MenuGroup, MenuItem } from '@wordpress/components';
+import { useState, useMemo } from '@wordpress/element';
 import { __ } from '@wordpress/i18n';
 import { useEntityRecord, store as coreStore } from '@wordpress/core-data';
 import { check } from '@wordpress/icons';
 import { store as noticesStore } from '@wordpress/notices';
 import { store as preferencesStore } from '@wordpress/preferences';
 
+/**
+ * Internal dependencies
+ */
+import PostPanelRow from '../post-panel-row';
+
 /**
  * Internal dependencies
  */
@@ -19,11 +25,6 @@ import ResetDefaultTemplate from './reset-default-template';
 import { unlock } from '../../lock-unlock';
 import CreateNewTemplate from './create-new-template';
 
-const POPOVER_PROPS = {
-	className: 'editor-post-template__dropdown',
-	placement: 'bottom-start',
-};
-
 export default function BlockThemeControl( { id } ) {
 	const {
 		isTemplateHidden,
@@ -63,6 +64,21 @@ export default function BlockThemeControl( { id } ) {
 		[]
 	);
 
+	const [ popoverAnchor, setPopoverAnchor ] = useState( null );
+	// Memoize popoverProps to avoid returning a new object every time.
+	const popoverProps = useMemo(
+		() => ( {
+			// Anchor the popover to the middle of the entire row so that it doesn't
+			// move around when the label changes.
+			anchor: popoverAnchor,
+			className: 'editor-post-template__dropdown',
+			placement: 'left-start',
+			offset: 36,
+			shift: true,
+		} ),
+		[ popoverAnchor ]
+	);
+
 	if ( ! hasResolved ) {
 		return null;
 	}
@@ -90,60 +106,62 @@ export default function BlockThemeControl( { id } ) {
 		}
 	};
 	return (
-		<DropdownMenu
-			popoverProps={ POPOVER_PROPS }
-			focusOnMount
-			toggleProps={ {
-				size: 'compact',
-				variant: 'tertiary',
-				tooltipPosition: 'middle left',
-			} }
-			label={ __( 'Template options' ) }
-			text={ decodeEntities( template.title ) }
-			icon={ null }
-		>
-			{ ( { onClose } ) => (
-				<>
-					<MenuGroup>
-						{ canCreateTemplate && (
+		<PostPanelRow label={ __( 'Template' ) } ref={ setPopoverAnchor }>
+			<DropdownMenu
+				popoverProps={ popoverProps }
+				focusOnMount
+				toggleProps={ {
+					size: 'compact',
+					variant: 'tertiary',
+					tooltipPosition: 'middle left',
+				} }
+				label={ __( 'Template options' ) }
+				text={ decodeEntities( template.title ) }
+				icon={ null }
+			>
+				{ ( { onClose } ) => (
+					<>
+						<MenuGroup>
+							{ canCreateTemplate && (
+								<MenuItem
+									onClick={ () => {
+										onNavigateToEntityRecord( {
+											postId: template.id,
+											postType: 'wp_template',
+										} );
+										onClose();
+										mayShowTemplateEditNotice();
+									} }
+								>
+									{ __( 'Edit template' ) }
+								</MenuItem>
+							) }
+
+							<SwapTemplateButton onClick={ onClose } />
+							<ResetDefaultTemplate onClick={ onClose } />
+							{ canCreateTemplate && (
+								<CreateNewTemplate onClick={ onClose } />
+							) }
+						</MenuGroup>
+						<MenuGroup>
 							<MenuItem
+								icon={ ! isTemplateHidden ? check : undefined }
+								isSelected={ ! isTemplateHidden }
+								role="menuitemcheckbox"
 								onClick={ () => {
-									onNavigateToEntityRecord( {
-										postId: template.id,
-										postType: 'wp_template',
-									} );
-									onClose();
-									mayShowTemplateEditNotice();
+									setRenderingMode(
+										isTemplateHidden
+											? 'template-locked'
+											: 'post-only'
+									);
 								} }
 							>
-								{ __( 'Edit template' ) }
+								{ __( 'Show template' ) }
 							</MenuItem>
-						) }
-
-						<SwapTemplateButton onClick={ onClose } />
-						<ResetDefaultTemplate onClick={ onClose } />
-						{ canCreateTemplate && (
-							<CreateNewTemplate onClick={ onClose } />
-						) }
-					</MenuGroup>
-					<MenuGroup>
-						<MenuItem
-							icon={ ! isTemplateHidden ? check : undefined }
-							isSelected={ ! isTemplateHidden }
-							role="menuitemcheckbox"
-							onClick={ () => {
-								setRenderingMode(
-									isTemplateHidden
-										? 'template-locked'
-										: 'post-only'
-								);
-							} }
-						>
-							{ __( 'Show template' ) }
-						</MenuItem>
-					</MenuGroup>
-				</>
-			) }
-		</DropdownMenu>
+						</MenuGroup>
+					</>
+				) }
+			</DropdownMenu>
+		</PostPanelRow>
 	);
 }
diff --git a/packages/editor/src/components/post-template/classic-theme.js b/packages/editor/src/components/post-template/classic-theme.js
index 4345e06211c661..6cef7d1582abd2 100644
--- a/packages/editor/src/components/post-template/classic-theme.js
+++ b/packages/editor/src/components/post-template/classic-theme.js
@@ -16,11 +16,7 @@ import { store as noticesStore } from '@wordpress/notices';
 import { store as editorStore } from '../../store';
 import CreateNewTemplateModal from './create-new-template-modal';
 import { useAllowSwitchingTemplates } from './hooks';
-
-const POPOVER_PROPS = {
-	className: 'editor-post-template__dropdown',
-	placement: 'bottom-start',
-};
+import PostPanelRow from '../post-panel-row';
 
 function PostTemplateToggle( { isOpen, onClick } ) {
 	const templateTitle = useSelect( ( select ) => {
@@ -216,17 +212,37 @@ function PostTemplateDropdownContent( { onClose } ) {
 }
 
 function ClassicThemeControl() {
+	const [ popoverAnchor, setPopoverAnchor ] = useState( null );
+	// Memoize popoverProps to avoid returning a new object every time.
+	const popoverProps = useMemo(
+		() => ( {
+			// Anchor the popover to the middle of the entire row so that it doesn't
+			// move around when the label changes.
+			anchor: popoverAnchor,
+			className: 'editor-post-template__dropdown',
+			placement: 'left-start',
+			offset: 36,
+			shift: true,
+		} ),
+		[ popoverAnchor ]
+	);
+
 	return (
-		<Dropdown
-			popoverProps={ POPOVER_PROPS }
-			focusOnMount
-			renderToggle={ ( { isOpen, onToggle } ) => (
-				<PostTemplateToggle isOpen={ isOpen } onClick={ onToggle } />
-			) }
-			renderContent={ ( { onClose } ) => (
-				<PostTemplateDropdownContent onClose={ onClose } />
-			) }
-		/>
+		<PostPanelRow label={ __( 'Template' ) } ref={ setPopoverAnchor }>
+			<Dropdown
+				popoverProps={ popoverProps }
+				focusOnMount
+				renderToggle={ ( { isOpen, onToggle } ) => (
+					<PostTemplateToggle
+						isOpen={ isOpen }
+						onClick={ onToggle }
+					/>
+				) }
+				renderContent={ ( { onClose } ) => (
+					<PostTemplateDropdownContent onClose={ onClose } />
+				) }
+			/>
+		</PostPanelRow>
 	);
 }
 
diff --git a/packages/editor/src/components/post-template/panel.js b/packages/editor/src/components/post-template/panel.js
index 903612ef11ed15..0bc86695fb8020 100644
--- a/packages/editor/src/components/post-template/panel.js
+++ b/packages/editor/src/components/post-template/panel.js
@@ -2,7 +2,6 @@
  * WordPress dependencies
  */
 import { useSelect } from '@wordpress/data';
-import { __ } from '@wordpress/i18n';
 import { store as coreStore } from '@wordpress/core-data';
 
 /**
@@ -11,7 +10,6 @@ import { store as coreStore } from '@wordpress/core-data';
 import { store as editorStore } from '../../store';
 import ClassicThemeControl from './classic-theme';
 import BlockThemeControl from './block-theme';
-import PostPanelRow from '../post-panel-row';
 
 /**
  * Displays the template controls based on the current editor settings and user permissions.
@@ -65,19 +63,11 @@ export default function PostTemplatePanel() {
 	}, [] );
 
 	if ( ( ! isBlockTheme || ! canViewTemplates ) && isVisible ) {
-		return (
-			<PostPanelRow label={ __( 'Template' ) }>
-				<ClassicThemeControl />
-			</PostPanelRow>
-		);
+		return <ClassicThemeControl />;
 	}
 
 	if ( isBlockTheme && !! templateId ) {
-		return (
-			<PostPanelRow label={ __( 'Template' ) }>
-				<BlockThemeControl id={ templateId } />
-			</PostPanelRow>
-		);
+		return <BlockThemeControl id={ templateId } />;
 	}
 	return null;
 }