Index: customize-controls.js
===================================================================
--- customize-controls.js	(revision 23258)
+++ customize-controls.js	(working copy)
@@ -886,6 +886,11 @@
 			event.preventDefault();
 		});
 
+        $('.upload-dropzone a.upload').keydown( function( event ) {
+            if ( 13 === event.which ) // enter
+                this.click();
+        });
+
 		$('.collapse-sidebar').on( 'click keydown', function( event ) {
 			if ( event.type === 'keydown' &&  13 !== event.which ) // enter
 				return;