Gauthier, who also had an assist, turned and scored after a loose puck came to him alone in front of the net.
Jackson LaCombe and Troy Terry also each had a goal and an assist, and Olen Zellweger scored for the Ducks (14-7-1), who have won three of four. Lukas Dostal made 29 saves.
Shea Theodore, Braeden Bowman and Tomas Hertl scored, and Jack Eichel had two assists for the Golden Knights (10-4-7), who extended their point streak to six games (3-0-3). Akira Schmid made 28 saves.
Theodore gave Vegas a 1-0 lead at 3:25 of the first period, taking advantage of a screen by Bowman to score on a one-timer from just inside the blue line.
Bowman extended it to 2-0 at 4:37 with a goal in his third straight game. He was in front of the crease when he scored on a loose puck with a backhand, his fourth goal in his sixth NHL game.
The Ducks then scored two goals 34 seconds apart to tie it 2-2.
LaCombe cut it to 2-1 at 7:43 on a one-timer from above the right circle after Vegas defenseman Noah Hanifin broke up a breakaway by Beckett Sennecke, who was able to retrieve the puck and find LaCombe.
Zellweger tied it 2-2 at 8:17 when he hit the top right corner of the net with a wrist shot from the left circle off a rush.
Hertl’s power-play goal moved the Golden Knights back in front 3-2 at 17:59, scoring on a tip from in front of the crease.
Terry tied it 3-3 at 13:50 of the second period when he scored off a feed from Leo Carlsson to finish a 2-on-1 rush.
