Mario Kart 8 and BotW. Those are the best Nintendo games, IMO. And, since they're sequels by most definitions.......

Super Mario Bros 3. Just compare the first 2 (well, the first 2 that came out in Japan, meaning 1 and The Lost Levels. Though even if we include the Doki Doki Panic spinoff SMB2, it still holds true) with what the 3rd one brought to the table. Super Mario wolrd expended further on this, but didn't revolutionize like 3 did.

Then, there's SSB Melee. It improves the original vastly in every which way and then some.

Finally, Mario Kart: Double Dash. Vastly more drivers, more items, and especially some grand battle modes

Oh, and did you notice that Nintendo manages to pull this off with 3rd party IPs too? Hyrule Warriors is among the very best Mosou games, and the Raving Rabbits where dead and buried in Rabbits Land until Mario & Rabbits came along.

I think the original post makes it very clear that "sequel" in this sense has NOTHING TO DO WITH NARRATIVE

My vote would be for Wind Waker. I think the leap from N64 to Gamecube was just glorious. The world is massive, seamless, and searching for Islands provided this sense of exploration and discovery I had never felt before in a game and really took those Zelda aspects to a new level.

I've played it through 3 times and will no doubt do so again.

I'm only holding off on replaying the HD version cause I want them to port that to Switch.

Direct sequel:
Ocarina of Time to Majora's Mask

Non-Direct Sequel:
Breath of the Wild

A Link to the Past. Zelda 2 on NES to this was just a huge jump plus its my favorite game of all time. Starfox to Starfox 64 is another plus Smash bros 64 to Melee is another good answer I would say. These are not direct sequels though

Star Fox Grand Prix

Yeah by that logic Smash 4 is a Namco game.

Super Mario Bros 3
DKC 2