All one may do is assess facts and seek a logical range of possibilities. Here are a few assessments of my own, FWIW:
First, yes, God may have intervened in some mysterious, hidden way but that will likely never be ascertained. In this life, anyway.
Second, since (a) Syria is a client state of long-standing with Russia and (b) Putin is not likely desirous of a direct conflict with the US or any NATO power, if for purely economic and no other reason, then it appears reasonable to assume that Russia was looking for a sensible alternative to war and found it; rather easily, actually.
Third, as the degree of difficulty inherent in "standing up" to a US president whose credibility, manliness and intellectual abilities are the stuff of ridicule on every continent was minimal, it probably looked to the SVR (Russian Foreign Intelligence) like a safe play.
I would like nothing more than to learn, however one does that, that God was so "pleased" with the "interfaith prayer event" and the intensity of the pope's own pleas that He "inspired" the Russian president to take the right ameliorative steps to scale the crisis down. Anything is possible. Even the far-flung unlikelihood that Obamster would even listen to common sense, which, it seems, is precisely what occurred (although his alternatives, in the light of plummeting popularity polls, were grim ones) might add weight to such a conclusion.
However, I don't expect anyone will learn that and we should remain grateful that the McCain-Oblahblah war party was - somehow - defeated without a shot being fired.