Tough to pick just one.
Street Fighter II and its variants gave SNES a big advantage over Mega Drive.
Just Dance and its spin-offs and sequels helped interest in Wii (which was already popular granted). It even got supported as a series longer on Wii than Wii U.
Minecraft has sold well on Switch, and who knows how well it could've done on Wii U if it was a launch title.

This!!

....along with Secret of Mana!! One of the best and earliest co-op RPG experience I've played.

Strong Candidates:

• Xevious (NES) - Easy to overlook nowadays, but the success of Xevious in Japan led to the Famicom actually selling reasonable numbers in Japan, along with attracting lots of third party support for possibly the first time for a Japanese game console. The Famicom started with a couple of Nintendo arcade ports and reached the big leagues with Super Mario Bros, but Xevious was what bridged that gap.
• Dragon Quest I/II/III (NES) - Made Nintendo the home of the most popular genre in Japan for a decade. 
• Street Fighter II (SNES) - Adding up the various SF2 versions on SNES, the game sold over 12 million copies, an attach rate of roughly 1 in 4 SNES owners. This was what kept the Genesis from completely defeating the SNES in America during the window of 1992 to 1994.
• Just Dance 2/3/onwards (Wii) - In the Wi's latter days, as well as during the Wii U's lifespan, it was the Just Dance series that kept casual Wii owners playing every so often. Just Dance 3 was the best-selling Wii game released after NSMB Wii, and according to old VGChartz estimates, new entries sold at least a million each year until the Switch era.
• Monster Hunter 4 (3DS) - This was the game that killed PlayStation's handhelds, albeit indirectly.

Good call; IIRC, up until the Switch, Just Dance 3 was the best selling third party game ever on any Nintendo platform.

Yeah 3DS snatching MH away from Sony that gen was a fatal blow; without it, Vita was dead in the water.

Dragon Quest, Teenage Mutant Ninja Turtles (NES), Final Fantasy, Megaman (series), Castlevania, Street Fighter II.

I'm fairly sure that Rare was considered a second party developer for Nintendo with the release of DKC.  I could be wrong though.

I think Street Fighter II is a good candidate. The only third party system seller I can think of that did well world wide.
As much as the SNES JRPGs have gotten astounding critical acclaim and lasting reputation, they didn’t sell all that well outside of Japan at the time (save maybe FFVI to an extend), most of them didn’t even release in Europe.
I do think one can mention the Dragon Quest franchise though, as it stock to the Nintendo systems as their primary console and have sold consistently well there. Final Fantasy moved to Playstation when that series got really big.

The Monster Hunter games and Just Dance are also undeniable choices of course.

Resident Evil 4 is of course iconic, but it didn’t really do much for the Gamecube and got easily outsold by the ports.

Of all time? Probably one of the early Dragon Quest or Final fantasy games given they had an impact on multiple generations. Or Monster Hunter 3 since that series jumping to Nintendo - for a time, exclusively - was big.  This is a much more interesting question on a per generation basis though because the answers become so wildly different.

For example, I would say Dragon Quest or Final Fantasy would take the cake for the NES and then Final Fantasy VI for the SNES, but then on the N64 I instinctively go for Doom 64. Having the official sequel to Doom and Doom 2 as an N64 3rd party exclusive really cemented the system as a heavy hitter in the emerging shooter genre. And then Resident Evil 4 on the GameCube is probably the biggest given the cultural impact since no game really transformed the sales trajectory. Wii is Monster Hunter 3, that series jumping to Nintendo was huge. Wii U is probably an indie game, maybe Fast Racing Neo as that really gave a lot of momentum to Shin'en, or Shovel Knight because it is kind of emblematic of Nintendo's embracing of indies as a big part of their library. Switch I think it's Doom 2016, no contest. That was the game that came out and everyone sat up and paid attention and was the beginning of Nintendo recovering the third party support lost over the course of the late Wii and Wii U eras.

Yeah. It's a gray area. According to the internet and a quick search, it seems Nintendo only bought up around 25% of Rare's shares AFTER the game launched and became a massive success. Then they bought up more stock. And it wasn't until 1995 that they became a majority holder.

So even Nintendo was not immune to the mightiness of DK1.

The Super NES was very third party driven, 3rd party software sold more than Nintendo's games by a good margin.