In terms of how much it contributed the platform's success, which do you think was the most important third party title ever on a Nintendo platform, and what's your reasoning?

Tetris is thrid-party, right? If so then I’d go with that. The game was a huge contributors to GameBoy’s success, launching Nintendo into their dominant position over the handheld market.

Technically the GB version was developed by Nintendo IIRC

https://en.wikipedia.org/wiki/Tetris_(Game_Boy_video_game)

madworld. put to bed the idea that the wii is for grandmas and newborns. finally we got a hardcore game.

Final Fantasy & Dragon Quest. It made Famicom the number one system in Japan and FF esp helped popularize RPGs in the west. (not to the extent of FF7 that came years later tho). I do want to give a shoutout to Capcom tho with Mega Man. Konami with Castlevania. Tecmo with Ninja Gaiden. Series that defined third party hits like no other before it. Franchises that are still around. Even if some began in arcades like Ninja Gaiden or Haunted Castle. They were defined on NES. Final Fantasy tho is one of the earlier examples of other companies chasing that success. SEGA created Phantasy Star. Master System also got Miracle Warriors. Square helped define SNES as a RPG powerhouse. They don't get there without Final Fantasy and DQ. Now DQ wasn't popular in the west. Nintendo Power gave away the game for free. In Japan it became the most popular series there.

I don't know if the most important, but I believe StreetFighter2 was a console seller.

Can't argue with this. Final Fantasy in especial, it gave a Crown of RPG king for SNES! 

Looking all these games, you can't help but notice how the N64 let its partners down...

Final Fantasy VII–IX, Castlevania: SotN, Mega Man X4–X6, and many others...

The very partners that had cemented Nintendo's success also helped PlayStation to crush the N64 and become the first +100M console. Sticking with cartridges and passing production costs on to partners was one of the biggest mistakes ever made in the industry...

This should be the answer! I was there and saw it. Many people that I knew were saving for a Genesis-Mega Drive, and totally changed their minds once they saw SFII. Back in the NES, many answers could be right, as already stated here. But SNES was lagging behind, Genesis was indeed a great console that had brought that 'arcade at home' feel (Altered Beast, Strider), and that kinda changed the game (pun not intended). This was the most 'system seller' game I ever saw on a Nintendo console and helped it win the war with Sega at the time.

Easily Monster Hunter 3 Ultimate.

It was the stab in the heart of the Vita and allowed the 3DS to have a safe journey after a rocky start, which would be quite important since it was the one thing stopping Nintendo form bleeding money. Nintendo lost money for 3 years straight, but not much. If the 3DS was not as successful, things would be dire.

Resident Evil 4 immediately comes to mind. May not have been a huge system seller overall, but to me, the game is synonymous with the GameCube. Helps that it's one of the best games of all time.