Dallas got two quick ones in the second to take the lead, the first coming from Miro Heiskanen on the power play and the next courtesy of a Blake Comeau tap-in on the rush just two minutes later.
The Stars made it 3-1 on another power play on a snipe from the right wing by Alexander Radulov that found the top corner far side.
But Anaheim came surging back with five unanswered and dominated the third period from start to finish.
"We just established what we wanted to do," Getzlaf said. "We showed glimpses of it throughout the game, but the third period we came out and executed the way we wanted to on our forecheck as well as getting the puck out of our zone."
After going 3-1-0 on their recent homestand, they hit the road for five straight starting Saturday in Columbus.