diff --git src/wp-admin/includes/update-core.php src/wp-admin/includes/update-core.php
index a5947e871e..5f5f30bfc3 100644
--- src/wp-admin/includes/update-core.php
+++ src/wp-admin/includes/update-core.php
@@ -1179,7 +1179,11 @@ function update_core( $from, $to ) {
 		if ( ! $wp_filesystem->exists( $old_file ) ) {
 			continue;
 		}
-		$wp_filesystem->delete( $old_file, true );
+
+		// If the file isn't deleted, try writing an empty string to the file.
+		if ( ! $wp_filesystem->delete( $old_file, true ) && is_file( $old_file ) ) {
+			$wp_filesystem->put_contents( $old_file, '' );
+		};
 	}
 
 	// Remove any Genericons example.html's from the filesystem