Stastny scored on a 2-on-0 rush with Nate Schmidt for his 700th NHL point.
Malcolm Subban made 31 saves for his first win of the season in seven games for the Golden Knights (12-11-4), who ended their three-game winless streak (0-2-1).
"I've been in this league long enough to know there's certain games every year that maybe you should win or shouldn't win, or you win a different way, or something happens in the game and brings the guys together," Stastny said. "It's a game like this where you score late in a tough environment on the road right before Thanksgiving and feel good about yourselves. That's what we've got to do, but we know tomorrow we get back to work."
WATCH: [All Golden Knights vs. Predators highlights]
The Predators (11-9-4) lost for the first time in three games.
"The first 10 minutes were pretty even," Nashville forward Matt Duchene said. "They get kind of a lucky goal, and they're up. I thought we took over from there. I thought the last 50 minutes of the game was all us. They had a little push at the end, obviously, and ended up finding one with 0.2 or 0.3 seconds left. It's crazy. We play such a good game, and we don't get rewarded with two points."
Pacioretty tied it on a shot from the slot. Mark Stone made a drop pass to get the puck to Pacioretty, who beat the buzzer with a wrist shot.