No, but it can cement a consoles longevity. Read: Halo: Combat Evolved.

Without it, you don't have Xbox or Halo 2, which in itself was the prototype for what Xbox Live became on the Xbox 360.

Oh, in case anyone thinks I'm full of BS, here's a photo of my copy of SF2. Anyone wanna buy it?  I would sell it for cheap money.

Maybe, if it's relatively even until that one game, but it won't bring an underdog to victory. If Halo didn't do it back in the day, then what could?

Zkuq, in my opinion, SF2 won the console war for SNES over the Genesis.  I was a proud Genesis owner until that game came out.

Bottom line, I believe the SNES version of SF2 is way better than the Genesis one. Just my 2 cents.

Could one game change the fate of a console drastically from flop to best selling, probably not. Can it give the edge over other consoles and get a win? Yes. I think we've seen that games like DKC edged SNES over Sega. FF7 definitely gave the PS1 momentum in Japan and ousted the N64. BoTW was absolutely the catalyst for the Switch's success.

So yes one game can spark something but all those consoles (SNES, PS1, Switch). While they all had a lot more to offer, the timing (launch title / swan song) or circumstances (taking an exclusive away) can definitely flip momentum. Heck Xbox One's used games policy literally lost them that gen. Perceptions can flip in any given moment

Tell that to Nintendo and BotW.
That game alone carried Switch to 10m, so its possible for one game to carry whole generation. Yes it later got more games but if BotW wasnt huge success who knows what would happen to Switch. If people counted Switch as competitor to PS4 and One then i would say that BotW won that war for Nintendo but people dont count Nintendo as competitor to these 2.
Also original Xbox had Halo, that game alone put Xbox on the map. So yes one game can carry console but i dont think one game can win console war.

Super Mario 64 carried Nintendo 64 for a while and games like Mario Kart and Ocarina of Time assured the system did not fail despite its underwhelming lifetime sales.

Yeah. One or two games can carry a console for a time to get people to buy it but as you said they can't win a console war. 

As someone mentioned Wii Sports is the only thing that has come close but even with it Zelda, mario kart, novelty, price and timing had a large hand in it so to answer the thread no. Or at least as I know gaming from 4th gen onward, definetly not anytime recently. Perhaps Pong sold ever Atari, I know not. 

Technically, ColecoVision was kicking the living shit out of the Atari due to superb Donkey Kong arcade port being bundled with it. But then the US game crash came and everything collapsed, so it was not long lived.