Yes, especially in the latter half of the 14th century (when the Russian principalities began to gain in power). In the 1380's, one Khan (
Tokhtamysh) was finally able to consolidate power and deal a
major defeat to Moscow-but he proceeded to start a war with Timur (yes, that Timur), who invaded the Golden Horde and burned many of its major cities (including the capital, Sarai). The Horde never really recovered, and just a few decades later broke apart into four smaller Khanates (Kazan, Crimea, Astrakhan, and the rump Golden Horde) that Muscovy ate one by one.
So I think the best POD to save the Golden Horde is one internal to it-having Tokhtamysh not start a war with Timur, and having his son and grandson (at least) be reasonable competent as well would definately help things.