diff --git a/wagtail/admin/static_src/wagtailadmin/js/vendor/jquery.fileupload.js b/wagtail/admin/static_src/wagtailadmin/js/vendor/jquery.fileupload.js
index 71d0b3f737..85ff90546e 100644
--- a/wagtail/admin/static_src/wagtailadmin/js/vendor/jquery.fileupload.js
+++ b/wagtail/admin/static_src/wagtailadmin/js/vendor/jquery.fileupload.js
@@ -919,7 +919,7 @@
                 if (this.options.limitConcurrentUploads > 1) {
                     slot = $.Deferred();
                     this._slots.push(slot);
-                    pipe = slot.pipe(send);
+                    pipe = slot.then(send);
                 } else {
                     this._sequence = this._sequence.then(send, send);
                     pipe = this._sequence;
@@ -1090,7 +1090,7 @@
                 $.map(entries, function (entry) {
                     return that._handleFileTreeEntry(entry, path);
                 })
-            ).pipe(function () {
+            ).then(function () {
                 return Array.prototype.concat.apply(
                     [],
                     arguments
@@ -1159,7 +1159,7 @@
             return $.when.apply(
                 $,
                 $.map(fileInput, this._getSingleFileInputFiles)
-            ).pipe(function () {
+            ).then(function () {
                 return Array.prototype.concat.apply(
                     [],
                     arguments