2D Metroidvanias were few and far between before Dust: An Elysian Tail and half the indie community seemed to jump onboard.

I’d also give some credit to Ni no Kuni which came out in the last year of 7th gen and was a success. It had a part in kickstarting the genre. 

Panzer Korps has revived the old genre of the Hex Wargames which was killed 20 years before it's release by the rise of RTS games.

And while no game, Homestuck's storytelling has certainly had a big influence on the resurgence of Text Adventures. The fact that many of them release on Smartphones is also due to them being able to make long games without taking up much space or needing much power, helping it further to come back.

New Super Mario Bros.

Although not at the same level, Street Fighter 4 saved 2D fighting games from ending in the same pit as shoot em ups are.

Edit - Damn you, @Salnax!

Although Ni No Kuni is somewhat turn based, it's a weird mix between real time and turns. My case was more for the 100% turn based JRPGs, so I left it out. 

Black Flag. The previous AC games were gradually getting less and less fun and more glitchy, especially 3, but then Black Flag came out of nowhere, stunning many of us and turning people not fans of the series (like me) into huge fans of open world games like that. Then they changed genres to a more RPG style for Origins and Odyssey and forgot about Black Flag until announcing Skull and Bones and subsequently not doing anything with that since announcement. Super annoying.

Xenoblade. It really felt fresh in 2011. It took some western influences. Mixed them with traditional JRPG formula. Add a really good story and a massive unique world to explore and a great cast. All in a time where the JRPG genre was struggling badly. Not just in sales but in overall quality and budgets.

Street Fighter II. Fighting games existed before this but few were any good. Street Fighter II set the groundwork for most fightings games after then and to this day.

I wouldn't call that a genre saving game though. Popularity for open world action games hasn't dwindled at all. That game might have saved Assassin Creed franchise though from falling.

In the same year (2013) Saints Row IV and GTA V released.

It was announced years ago. The game doesn't need a 7 year development cycle. They clearly sat on it not knowing what to do. 

Well it's an assassination style genre I think it saved. But your probably right.