The defending Stanley Cup champion Ducks, on the brink of going home for the season, scored three times in the third period to break open a tight, physical game.
After Mike Ribeiro pulled the Stars within 3-2 at 4:41 of the third, defenseman O'Donnell built the lead back to two when he scored at 12:05. Todd Marchant added an empty-net goal with 1:24 remaining.
Jean-Sebastien Giguere made 40 saves for Anaheim, and Marty Turco had 27 for Dallas.
Chris Pronger and Chris Kunitz added two assists apiece for Anaheim.
Kunitz set up O'Donnell's score that gave the Ducks some breathing room. Behind the goal, Kunitz slid the puck to O'Donnell in front of the crease and he flicked a shot that went over the sprawling Turco's right leg.
Selanne had given the Ducks a 3-1 lead when they held a two-man advantage at 19:12 of the third. Pronger's slap shot from the right side bounced off the boards and the puck went straight to Selanne, who was parked on the left of the crease. Selanne one-timed it in before Turco had a chance to react.
Ribeiro got Dallas back into it - albeit not for long - when he scored on a fine individual play. He skated behind the Ducks' goal, feinted a wraparound to make Giguere commit, then stopped, spun around and flipped the puck over the sprawling goalie.
Getzlaf's power play goal gave Anaheim a 2-1 lead at 8:57 of the second. Getzlaf held the puck in the left circle, freezing defenseman Matt Niskanen, then wristed a shot between Niskanen's legs that sailed over Turco's left shoulder into the upper right corner of the net.
It was tied 1-1 at the end of an especially intense first period, when the Stars got off 15 shots, the Ducks 14, and both goalies made some spectacular saves.
Anaheim's Corey Perry, in his second game back from a lacerated tendon in his right leg, opened the scoring at 8:25 and Mattias Norstrom tied it at 18:27, just one second after a Dallas power play ended.
Perry, who led the Ducks in goals during the regular season but had been sidelined for six weeks, slid the puck between Turco's pads on a wrist shot from the right circle for his first goal of the series.
Norstrom's goal also was his first. He wristed a shot from the left circle over Giguere's right shoulder and just inside the left post.
Perry had just finished serving a roughing penalty after colliding with Turco behind the Dallas goal, when the Stars' goalie pinned against the boards, wrapped his arms around Perry. Players from both sides then tangled in a skirmish that led to a string of penalties.
Three Stars and four Ducks drew penalties, including 10-minute misconducts on Dallas' Brenden Morrow and Anaheim's Francois Beauchemin.
Among Turco's saves in the first was the time when, flat on his back, he raised his leg and the puck hit it and bounced away. Later in the period, when Teemu Selanne tried a wraparound, Turco was sprawled to the other side, but put his stick on the ice to stop the puck just before it crossed the goal line.
The puck was so close to being over the line that the play was reviewed, but the no-goal call was upheld.
At the other end, Giguere made a fine save when he went down to try to block a shot and reached out with his glove to bat the puck away. That began the sequence that led to Anaheim's first goal.
Notes: Only 20 of 219 teams have come back to win an NHL postseason series after being down 3-1. ... Dallas D Stephane Robidas left the ice to go to the locker room in the first period after he was struck by in the face by the puck, but he returned shortly afterward. ... The Ducks were without C Rob Niedermayer (concussion-like symptoms), and among those missing for Dallas was D Philippe Boucher (lower body injury). ... The Ducks reassigned RW Bobby Ryan to Portland of the AHL.