diff --git a/packages/block-library/src/post-content/index.php b/packages/block-library/src/post-content/index.php
index 228a0d52f40699..652c1b1fb87966 100644
--- a/packages/block-library/src/post-content/index.php
+++ b/packages/block-library/src/post-content/index.php
@@ -51,10 +51,33 @@ function render_block_core_post_content( $attributes, $content, $block ) {
 		$content .= wp_link_pages( array( 'echo' => 0 ) );
 	}
 
+	$filters_to_remove = array(
+		'wptexturize'            => false,
+		'shortcode_unautop'      => false,
+		'wp_filter_content_tags' => false,
+		'do_shortcode'           => false,
+		'convert_smilies'        => false,
+	);
+
+	// Temporarily remove some filters that are not suitable for this block.
+	foreach ( $filters_to_remove as $filter => &$priority ) {
+		$priority = has_filter( 'the_content', $filter );
+		if ( false !== $priority ) {
+			remove_filter( 'the_content', $filter, $priority );
+		}
+	}
+
 	/** This filter is documented in wp-includes/post-template.php */
 	$content = apply_filters( 'the_content', str_replace( ']]>', ']]>', $content ) );
 	unset( $seen_ids[ $post_id ] );
 
+	// Restore filters.
+	foreach ( $filters_to_remove as $filter => $priority ) {
+		if ( false !== $priority ) {
+			add_filter( 'the_content', $filter, $priority );
+		}
+	}
+
 	if ( empty( $content ) ) {
 		return '';
 	}
diff --git a/packages/block-library/src/template-part/index.php b/packages/block-library/src/template-part/index.php
index 838210480ca288..db50743d60f69f 100644
--- a/packages/block-library/src/template-part/index.php
+++ b/packages/block-library/src/template-part/index.php
@@ -127,20 +127,16 @@ function render_block_core_template_part( $attributes ) {
 			'';
 	}
 
-	// Run through the actions that are typically taken on the_content.
 	$seen_ids[ $template_part_id ] = true;
-	$content                       = do_blocks( $content );
-	unset( $seen_ids[ $template_part_id ] );
-	$content = wptexturize( $content );
-	$content = convert_smilies( $content );
-	$content = shortcode_unautop( $content );
-	$content = wp_filter_content_tags( $content );
-	$content = do_shortcode( $content );
 
 	// Handle embeds for block template parts.
 	global $wp_embed;
+	$content = $wp_embed->run_shortcode( $content );
 	$content = $wp_embed->autoembed( $content );
 
+	$content = do_blocks( $content );
+	unset( $seen_ids[ $template_part_id ] );
+
 	if ( empty( $attributes['tagName'] ) ) {
 		$defined_areas = get_allowed_block_template_part_areas();
 		$area_tag      = 'div';