Do you think that one single killer app can decide the outcome of a console war? If so, are there any times you consider this to have happened, and if not, why not?

No. Final Fantasy VII and Gran Turismo by themselves or maybe even combined weren't enough for PS1 to kick the butts of the competition. It was those titles, marketing, and even more titles that turned the tide.
One of the closest is Wii Sports. It was packed in with the console for years in all major regions except Japan. Wii Sports may be a tech demo, but there is hours of fun to have with it. Wii Sports was the flagship game that helped Wii become a phenomenon but did not win the "console war." Super Mario Galaxy, Mario Kart Wii, and Wii Sports Resort all helped Wii crack over 100 million units.

It's generally accepted that, at least in the US, DKC did for the SNES. But other than that, I can't think of another case where one game tilted the race so thoroughly.

Well, I must be older than you guys...because one game gets me...

Back in the years between 1990 to 1995, or so, it was Sega Genesis vs. Super Nintendo.

Genesis was kicking ass in the beginning, it had Sonic, Streets of Rage, a bloody Mortal Kombat, etc....

Street Fighter 2 changed all that....It was exclusive to SNES, and it dominated home video games.

Years later, after the Genesis lost that console war, it got a port of SF2...and it was lousy...How do I know? Hell, I bought it. 

Super Mario Bros

Wii Sports. Breath of the Wild. Super Mario 64. Super Mario Bros. These games single-handedly sent demand sky-high. Now, had there been literally no releases beyond this, then the systems would’ve all quickly faded out; however, the point I’m making is more that single system seller could be enough to send system sales figures to very high levels for as much as a year. Follow that up with another system seller not too long later, and the system has legs (SMGalaxy, SMOdyssey, Zelda OoT, The Legend of Zelda.).

Yeah to be clear, I meant it as "the presence of this one game could change which console wins", not "if the console only had this game and nothing else" haha

ah okay that makes more sense lol. Thank you for the clarification. I think BotW and Wii Sports definitely serve as strong examples to this question, single-handily sending Nintendo from a dying brand to a cultural sensation overnight.

Not anymore.

There's just too many games for anyone to just depend on one.

Console A is capable of selling 60 million.
Console B is capable of selling 100 million.

A full GTA exclusivity on console A may enable it to beat console B.

It depends on the natural sales gap between console A and B. If the gap is small, then the additional exclusivity of a single 15 million+ selling title will decide the winner. If it's big, then something like a GTA exclusivity will be needed.

But releasing a major exclusive early in the gen can have a profound domino effect. It helps make the console the go to platform for most games and invites more exclusives.