diff --git a/src/wp-includes/class-wp.php b/src/wp-includes/class-wp.php
index 8d67820545..0a0a501ee0 100644
--- a/src/wp-includes/class-wp.php
+++ b/src/wp-includes/class-wp.php
@@ -408,7 +408,8 @@ class WP {
 	 * If showing a feed, it will also send Last-Modified, ETag, and 304 status if needed.
 	 *
 	 * @since 2.0.0
-	 * @since 4.4.0 `X-Pingback` header is added conditionally after posts have been queried in handle_404().
+	 * @since 4.4.0 `X-Pingback` header is added conditionally for single posts that allow pings.
+	 * @since 6.1.0 Runs after posts have been queried.
 	 */
 	public function send_headers() {
 		$headers       = array();
@@ -504,6 +505,15 @@ class WP {
 			}
 		}
 
+		if ( is_singular() ) {
+			$post = isset( $wp_query->post ) ? $wp_query->post : null;
+
+			// Only set X-Pingback for single posts that allow pings.
+			if ( $post && pings_open( $post ) ) {
+				$headers['X-Pingback'] = get_bloginfo( 'pingback_url', 'display' );
+			}
+		}
+
 		/**
 		 * Filters the HTTP headers before they're sent to the browser.
 		 *
@@ -701,14 +711,9 @@ class WP {
 
 			if ( is_singular() ) {
 				$post = isset( $wp_query->post ) ? $wp_query->post : null;
-
-				// Only set X-Pingback for single posts that allow pings.
-				if ( $post && pings_open( $post ) && ! headers_sent() ) {
-					header( 'X-Pingback: ' . get_bloginfo( 'pingback_url', 'display' ) );
-				}
+				$next = '<!--nextpage-->';
 
 				// Check for paged content that exceeds the max number of pages.
-				$next = '<!--nextpage-->';
 				if ( $post && ! empty( $this->query_vars['page'] ) ) {
 					// Check if content is actually intended to be paged.
 					if ( false !== strpos( $post->post_content, $next ) ) {
@@ -770,14 +775,14 @@ class WP {
 
 		$parsed = $this->parse_request( $query_args );
 
-		$this->send_headers();
-
 		if ( $parsed ) {
 			$this->query_posts();
 			$this->handle_404();
 			$this->register_globals();
 		}
 
+		$this->send_headers();
+
 		/**
 		 * Fires once the WordPress environment has been set up.
 		 *
diff --git a/tests/phpunit/tests/wp/sendHeaders.php b/tests/phpunit/tests/wp/sendHeaders.php
new file mode 100644
index 0000000000..cc956409ef
--- /dev/null
+++ b/tests/phpunit/tests/wp/sendHeaders.php
@@ -0,0 +1,22 @@
+<?php
+
+/**
+ * @group wp
+ * @covers WP::send_headers
+ */
+class Tests_WP_SendHeaders extends WP_UnitTestCase {
+
+	/**
+	 * @ticket 56068
+	 */
+	public function test_send_headers_runs_after_posts_have_been_queried() {
+		add_action(
+			'send_headers',
+			function ( $wp ) {
+				$this->assertQueryTrue( 'is_front_page', 'is_home' );
+			}
+		);
+
+		$this->go_to( home_url() );
+	}
+}