"I got to take what he gives me and he was playing pretty deep in his net," Getzlaf said of his move that beat Dallas goaltender Kari Lehtonen. "He didn't give me much for the shot -- if the shot's there, I'm probably taking it, that's one of the other options."
Andrew Cogliano scored in regulation for Anaheim, which has won five in a row and gone nine games without a regulation defeat (7-0-2).
"Is it better to be good than lucky or is it better to be lucky or whatever the phrase is," Ducks coach Bruce Boudreau said. "But I mean, when you're playing really good, things seem to go off the post, because maybe that's all they have to shoot at. I'd rather take that than the alternative, because we've been on the other side of it."
Bobby Ryan also scored in the shootout, while Hiller stopped both Dallas shooters he faced.
"If you're fighting hard and doing the right things, things will go your way," said Hiller, who is 7-0-1 in his past eight outings.
"Definitely I feel pretty good right now and I'm confident in how I'm playing, but at the same time, I know I'm playing well because I'm battling, I'm pushing myself and that's when you get lucky."
Ray Whitney, in his second game back after missing 16 due to a broken foot, scored the only goal for the Stars, who have scored just two in their past three games.
Lehtonen, making his sixth straight start, had 29 saves.
Dallas was missing center Jamie Benn, who sat out his second straight game with a wrist injury, but had numerous opportunities that it didn't capitalize on, missing five breakaways, hitting three goalposts or crossbars and having what could have been the go-ahead goal disallowed.
"We had a lot of good chances, just kind of got the wrong side of the post on a few of them," said Dallas rookie Reilly Smith, who had two breakaways and rang another shot off the post.
"We have to start burying the puck because these last few games we haven't created enough offensive opportunities to put the puck in the back of the net."
With the game tied at 1 midway through the second period, the Stars had back-to-back opportunities to take the lead.
After entering the Anaheim zone on the rush, Whitney rolled the puck in on goal, but Hiller left a rebound in front.
Derek Roy pounced on it, popping it over Hiller's pads at 10:27 just as the whistle sounded, nullifying the goal.
"Those things are unfortunate. They happen, people make mistakes," said Dallas captain Brenden Morrow, who returned to the lineup after missing two games with a groin injury. "(Referee Marc Joannette) made a mistake there, he was a little quick on his whistle. But we needed to step up. We had plenty of opportunities to find one. We didn't. It's on us."
Just 38 seconds later, it looked as if Smith put Dallas ahead, but his in-close chip shot over Hiller's blocker ricocheted off the right post, pinged off the crossbar and bounced out behind Hiller.
An Anaheim turnover gave Dallas another breakaway with 6:21 left in the second, but Hiller made a nice save on Eric Nystrom's wrist shot.
Lehtonen made a nice stop on a Ducks power play with 2:17 remaining when he slid across the crease to stop Francois Beauchemin's one-timer from the right side of the crease.
With Dallas on the power play, Lehtonen came up with another big save 48 seconds into the final period when he slid across the crease to get his pad on rookie Emerson Etem's one-timer from the right circle.
The Stars appeared to take the lead again with 3:25 left in regulation, while on a power play, when Jaromir Jagr swiped a shot from the left side of the crease, while falling, past Hiller.
The horn sounded, Dallas players celebrated, but the officials waved it off and play continued for another 33 seconds before there was a video review. Replays clearly showed the puck hitting the right post and crossbar and never crossing the goal line.
"The one that the ref blew the whistle there, I thought I was definitely lucky, but on the other ones, both of the posts, I got a piece of it," Hiller said. "When you get those bounces and things hit you and hit the post and go out instead of hit you and hit the post and go in, definitely that makes you feel bigger. I felt pretty good there."
The Stars opened the scoring with Whitney getting his third goal of the season 12:35 into the opening period. After Alex Goligoski's wrist shot hit Loui Eriksson's skate in front, Whitney found the loose puck first, sending a backhand over Hiller's glove.
Hiller made a nice save after Whitney's cross-ice backhand pass on a 2-on-1 rush led to Eriksson's point-blank wrist shot 2:47 into the second.
Dallas had two good opportunities to seize a two-goal lead, but was unable to cash in when Smith sped in on a breakaway at 6:32, but his wrist shot sailed over the crossbar.
Just 12 seconds later, the Stars drove back into the Anaheim zone on a 2-on-1 rush that led to Roy's one-timer from the right faceoff circle, but Hiller made the save.
Less than a minute later, the Ducks tied it on Cogliano's 10th goal of the season.
After receiving a nice backhand pass from Peter Holland, Lehtonen made a great save on Cogliano's one-timer from in front, but Cogliano managed to jam home the loose rebound at 7:28.
Anaheim G Viktor Fasth sat out his second straight game with an upper-body injury and is listed day to day. Jeff Deslauriers, who was recalled from ECHL Fort Wayne on Tuesday, served as Hiller's backup. ... With the point for the shootout loss, Dallas is 6-0-2 in its past eight home games against Anaheim. ... The Ducks rallied to win their 13th game after trailing at any point in the game, equaling their total from all of last season. They are 11-2-1 when their opponent scores first. Those win totals are the most by any NHL club in the first 26 games of a season since 1987-88.