Pavel Mintyukov and Alex Killorn were called for penalties 17 seconds apart for the Ducks, and Tkachuk tipped in a wrist shot from Tim Stutzle on the two-man advantage to tie it 1-1 at 17:36.
Stutzle extended his point streak to seven games (three goals, six assists) with the assist, and Drake Batherson also earned an assist on the play to extend his point streak to seven games (two goals, seven assists).
The Ducks went back in front 2-1 with six seconds left when Jackson LaCombe scored on his own rebound from in close.
Tkachuk tied it 2-2 at 37 seconds of the second period, putting in his own rebound with a backhand after Dostal stopped his initial shot on a breakaway.
"They're a very good rush hockey team and they're going to be up and down the ice,” Terry said, “so [it’s] managing the game a little differently than when we're playing L.A. last game (a 2-1 loss to the Kings on Friday), and it's more physical in the corners. As a young team, it's just learning how to play in those different kinds of games."
Ullmark made the save on Vatrano's breakaway attempt at 1:18, 41 seconds after Tkachuk tied it, but Vatrano later scored on a loose puck in the slot to give Anaheim its third lead of the game, 3-2 at 4:37 of the third period.
Vatrano, who scored an NHL career-high 37 goals last season, has four goals in the past four games after scoring two in the first 18.
"I felt Frankie was going to score eventually," Ducks coach Greg Cronin said. "He's a scorer and those guys go through dry spells. ... It doesn't matter how many games you don't score. I just believe when you score goals and you have a history of doing it, you're eventually going to get rewarded, and that's what he's in right now."
