diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index 3c0e6d8b9f777..229c9a75416af 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -704,7 +704,8 @@
 add_action( 'rest_api_init', 'wp_oembed_register_route' );
 add_filter( 'rest_pre_serve_request', '_oembed_rest_pre_serve_request', 10, 4 );
 
-add_action( 'wp_head', 'wp_oembed_add_discovery_links' );
+add_action( 'wp_head', 'wp_oembed_add_discovery_links', 4 ); // Printed after feed_links() and feed_links_extra().
+add_action( 'wp_head', 'wp_oembed_add_discovery_links' ); // Unhooked the first time that wp_oembed_add_discovery_links() runs for back-compat.
 add_action( 'wp_head', 'wp_oembed_add_host_js' ); // Back-compat for sites disabling oEmbed host JS by removing action.
 add_filter( 'embed_oembed_html', 'wp_maybe_enqueue_oembed_host_js' );
 
diff --git a/src/wp-includes/embed.php b/src/wp-includes/embed.php
index c143ffe4a455d..b7567024aa194 100644
--- a/src/wp-includes/embed.php
+++ b/src/wp-includes/embed.php
@@ -332,8 +332,19 @@ function wp_oembed_register_route() {
  *
  * @since 4.4.0
  * @since 6.8.0 Output was adjusted to only embed if the post supports it.
+ * @since 6.9.0 Now runs first at `wp_head` priority 4, with a fallback to priority 10. This helps ensure the discovery links appear within the first 150KB.
  */
 function wp_oembed_add_discovery_links() {
+	if ( doing_action( 'wp_head' ) ) {
+		// For back-compat, short-circuit if a plugin has removed the action at the original priority.
+		if ( ! has_action( 'wp_head', 'wp_oembed_add_discovery_links', 10 ) ) {
+			return;
+		}
+
+		// Prevent running again at the original priority.
+		remove_action( 'wp_head', 'wp_oembed_add_discovery_links' );
+	}
+
 	$output = '';
 
 	if ( is_singular() && is_post_embeddable() ) {
diff --git a/tests/phpunit/tests/oembed/discovery.php b/tests/phpunit/tests/oembed/discovery.php
index 41efe1cc2a378..8f0cacaeb6004 100644
--- a/tests/phpunit/tests/oembed/discovery.php
+++ b/tests/phpunit/tests/oembed/discovery.php
@@ -49,6 +49,9 @@ public function test_add_oembed_discovery_links_to_post() {
 		$expected .= '<link rel="alternate" title="oEmbed (XML)" type="text/xml+oembed" href="' . esc_url( get_oembed_endpoint_url( get_permalink(), 'xml' ) ) . '" />' . "\n";
 
 		$this->assertSame( $expected, get_echo( 'wp_oembed_add_discovery_links' ) );
+
+		add_filter( 'oembed_discovery_links', '__return_empty_string' );
+		$this->assertSame( '', get_echo( 'wp_oembed_add_discovery_links' ), 'Expected filtering oembed_discovery_links to empty string to result in no wp_oembed_add_discovery_links() output.' );
 	}
 
 	public function test_add_oembed_discovery_links_to_page() {
@@ -100,4 +103,39 @@ public function test_wp_oembed_add_discovery_links_non_embeddable_post_type_outp
 
 		$this->assertFalse( get_oembed_response_data( $post, 100 ) );
 	}
+
+	/**
+	 * @ticket 64178
+	 * @covers ::wp_oembed_add_discovery_links
+	 */
+	public function test_wp_oembed_add_discovery_links_back_compat() {
+		$action       = 'wp_head';
+		$old_priority = 10;
+		$new_priority = 4;
+		$callback     = 'wp_oembed_add_discovery_links';
+
+		$this->assertTrue( has_action( $action, $callback, $old_priority ), 'Expected wp_oembed_add_discovery_links() to be hooked at wp_head with old priority.' );
+		$this->assertTrue( has_action( $action, $callback, $new_priority ), 'Expected wp_oembed_add_discovery_links() to be hooked at wp_head with new priority.' );
+
+		// Remove all wp_head actions and re-add just the later old one.
+		remove_all_actions( $action );
+		add_action( $action, $callback, $old_priority );
+		add_action( $action, $callback, $new_priority );
+
+		$post_id = self::factory()->post->create();
+		$this->go_to( get_permalink( $post_id ) );
+		$this->assertQueryTrue( 'is_single', 'is_singular' );
+
+		$mock_action = new MockAction();
+		add_filter( 'oembed_discovery_links', array( $mock_action, 'filter' ) );
+
+		$wp_head_output = get_echo( 'wp_head' );
+		$this->assertSame( 1, $mock_action->get_call_count() );
+
+		$expected  = '<link rel="alternate" title="oEmbed (JSON)" type="application/json+oembed" href="' . esc_url( get_oembed_endpoint_url( get_permalink() ) ) . '" />' . "\n";
+		$expected .= '<link rel="alternate" title="oEmbed (XML)" type="text/xml+oembed" href="' . esc_url( get_oembed_endpoint_url( get_permalink(), 'xml' ) ) . '" />' . "\n";
+
+		$this->assertSame( $expected, $wp_head_output, 'Expected wp_head output to be the same as the wp_oembed_add_discovery_links() output.' );
+		$this->assertSame( $expected, get_echo( $callback ), 'Expected wp_oembed_add_discovery_links() output to be the same as the wp_head output when called outside of wp_head.' );
+	}
 }