Tuch was the third and final Golden Knight to shoot after Anaheim goalie John Gibson, who finished with 40 saves, stopped attempts by Jonathan Marchessault and James Neal.
After Tuch's goal, Vegas goalie Malcolm Subban, who earlier stopped shots by Corey Perry and Rickard Rakell, made a pad save on Ondrej Kase to seal the win.
Neal, Oscar Lindberg and Erik Haula scored goals for Vegas (17-9-1), which improved to 11-2-0 at home this season.
Francois Beauchemin, Antoine Vermette and Perry scored for Anaheim (11-11-6).
Vegas dominated the first period, firing 19 shots on Gibson who had a handful of highlight-reel saves. But the Golden Knights broke through two goals in a 16-second span, both on rebounds by Neal, who floated a shot over a sprawled Gibson, and Lindberg.
But Anaheim tightened up defensively and answered three consecutive goals on just eight shots in the second period to take a 3-2 lead, holding the Golden Knights to just five shots, including none in the first 8 1/2 minutes.
Beauchemin started the comeback at 1:03 with a blast from the blue line that eluded Subban, who was screened by Vermette. Vermette tied it four minutes later when he deflected a blue line blast by defenseman Kevin Bieksa.
Perry then gave Anaheim the lead when broke in free after taking a long pass from center Adam Henrique and rifled a shot over Subban's right shoulder.
That lead held up until Neal stole the puck in the corner and passed it to Haula, who fired it between the post and Gibson's pad to make it 3-3 with 4:42 left in regulation.
NOTES: Anaheim RW Rickard Rakell, who leads the team with eight goals, returned to the starting lineup after missing five games with an upper-body injury. ... Ducks D Hampus Lindholm flew home before the game with an upper-body injury and could miss the team's games this weekend. Lindholm, who has three goals and five assists in 19 games, sat out the first seven games of the season recovering from offseason shoulder surgery and also missed a Nov. 15 game against Boston with a lower-body injury. To take Lindholm's spot in the lineup, the Ducks recalled D Jaycob Megna from San Diego of the AHL. ... Anaheim also was without D Jakob Silfverberg who missed his third straight game with an upper-body injury. Also scratched for the Ducks were D Korbinian Holzer and C Joseph Blandisi. D Jon Merrill and D Brad Hunt were scratched by the Golden Knights.