Dorofeyev converted his own rebound to stretch the lead to 3-1 at 4:29 of the third with his team-leading ninth goal of the season.
Vatrano scored on the rush with 13 seconds left for the 3-2 final.
"As a staff, we try to break it down into how [the opponent is] generating chances and I think tonight a lot of them came off our sticks," Cronin said. "Just faulty passes and maybe some poor decisions, but they worked hard. I can't fault that. They worked hard and put ourselves in position to tie the game."
This was the first stop of a two-game trip for the Golden Knights, whose fathers have joined them on the road. Vegas improved to 10-0-1 (plus-28 goal differential) in games with the players’ fathers in attendance.
"It always gets the juices flowing," Theodore said.
Vegas coach Bruce Cassidy credited the dads with sparking the Golden Knights two seasons ago.
The Golden Knights were on a four-game losing streak when the fathers joined the team for the final two games of the road trip in early February. Vegas won both, against the Nashville Predators and Minnesota Wild, by the score of 5-1.
"It sort of kickstarted us to the road to winning the Cup, to be honest," Cassidy said. "We finished strong the second half, started believing in each other again and the dads had a lot to do with that. ... Our guys obviously like playing in front of their dads."
NOTES: Vegas forward Grigori Denisenko had a team-high five hits while playing 8:27 in his season debut after being recalled from Henderson of the American Hockey League on Wednesday ... The Golden Knights have scored a power-play goal in 12 of 16 games this season. ... Dostal leads the NHL with 392 saves. ... Anaheim had won its previous three games against Vegas at Honda Center.