Tuch, who was born in Syracuse and grew up in Baldwinsville, New York, said he had around 30-40 friends and family at the game.
"I know what Madison Square Garden is, I know what it means to this city and everything so it's pretty cool not only to get the overtime winner but to score a goal in this building," Tuch said.
WATCH: [All Golden Knights vs. Rangers highlights]
Reilly Smith, Paul Stastny, William Carrier scored, and Marc-Andre Fleury made 27 saves for the Golden Knights (19-14-2), who extended their point streak to four games (3-0-1) and are 10-2-1 in their past 13 games.
Fleury got his 423rd NHL win, tying Tony Esposito for ninth on the all-time list.
"It's very humbling to be amongst those guys for sure," Fleury said. "From start to finish, we played a good game and we deserved that win."
Brady Skjei, Mika Zibanejad and Chris Kreider scored, and Henrik Lundqvist made 37 saves for the Rangers (14-13-5), who lost their third straight game and eighth in their past 10 (2-5-3). Kevin Hayes had three assists.
"I think the first two periods (outshot 28-17), it's not the way we can play," Lundqvist said. "Not at home in front of our fans. We need to work harder. We can't accept not being ready to fight for one another here; I thought we were not ready."
Skjei gave the Rangers a 1-0 lead 1:13 into the first period converting on a 2-on-1 with Pavel Buchnevich.