Kyle Palmieri had the lone goal for the Ducks, which came 57 seconds into the third period. Palmiere, who had 21 points in 42 games last season, beat Varlamov on a breakaway to make it 1-1.
Palmieri's goal was set up by Ducks defenseman Francois Beauchemin, who played his first game since reconstructive surgery on his right knee.
"It was good to take a regular shift, give hits and take hits," Beauchemin said. "It's been a long summer, and I haven't had a chance to play any scrimmages during training camp. That was my first real game-type situation. It was good to play out there tonight."
"We played really well in the first, but we let the game get away from us afterwards," Hiller said. "I thought I had a couple good saves, but it's always a disappointment if you lose."
Anaheim right wing Jakob Silfverberg left in the third period with an apparent lower-body injury.
"He got banged up. Right now, it's day-to-day," Ducks coach Bruce Boudreau said. "Like all our injuries, we seem to have an awful lot of banged up guys that are not long term. They're just banged up. Hopefully, within the next two to three days, they'll all be skating, and within a week they'll be right in game shape and ready to go."