Cutter Gauthier extended the lead to 3-0 at 4:32, scoring a power-play goal with a snap shot short side from the right circle.
"In hindsight, that's the one that hurt us. It should have never went in the net," Vegas coach Bruce Cassidy said. "We needed that (save) at the end of the day if we were going to get points tonight."
Marner scored for the third straight game to make it 3-1 at 9:47 of the second. Stone's centering pass from behind the net hit off the skate of Ducks defenseman Ian Moore at the left post and deflected toward the other side of the crease, where Marner shot it into an open net.
Barbashev also scored for the third straight game to cut it to 3-2 at 10:40 of the third period. Dostal saved Barbashev's initial one-timer from in close, but the puck trickled behind him, allowing Barbashev to jam it across the goal line.
"You know they're going to press," Anaheim coach Joel Quenneville said. "They're going to be pressing offensively, gambling a little bit, taking the offensive side of a lot of pucks, and I think some of the clears we weren't great at, but at the same time, that's what you do when you're down, you take some risks and there are some rewards at the other end of it if you get through it."
Poehling scored into an empty net to make it 4-2 at 18:53 before Hertl scored with six seconds left for the 4-3 final.
"It seems like over the past little bit we've been chasing way too much and we've been relying on our comebacks," Theodore said. "It's not good enough. We have to start better."
NOTES: Anaheim swept the season series against Vegas for the first time. ... Ducks forward Mason McTavish returned after missing five games with an upper-body injury. He was a minus-2 with three shots in 14:46 of ice time.