The Stars hadn't won since beating Edmonton 4-1 on Jan. 7; the Ducks had gone 8-0-1 since a 3-1 loss to San Jose on Jan. 4.
"I thought we got out-chanced in this game, but our best player was our goalie," Dallas coach Glen Gulutzan said. "It was a good game to get."
The shutout was the 18th of Lehtonen's career, but his first since April 5, 2011 against Columbus -- a span of 32 games. He had lost his last four starts.
Dallas (25-21-2) scored the only goal of the game when Goligoski's long slap shot deflected off the hip of Anaheim's Cam Fowler and landed in the back of the Ducks' net. Goligoski's goal came just one day after he received a four-year contract extension from the Stars.
"It was kind of a broken play … three or four guys were in front of me," Fowler said. "I didn't even see the shot come. I don't know what I would have done differently to avoid it."
Assisting on the tally was Dallas center Mike Ribeiro, who was seeing his first action in seven games after going down with a knee injury during the win over the Oilers 17 days ago.
Gulutzan was definitely glad to have Ribeiro back on the ice against the Ducks.
"His knee's not as good as everybody thinks, but he gutted it out," Gulutzan said. "He's a competitive guy and he's an important guy to us. He spoke a lot on the bench and that helped us tonight."
Just 1:18 into the second period, the Stars nearly took a two-goal lead when a shot by Loui Eriksson got past Ducks goaltender Jonas Hiller. However, center Saku Koivu swooped in to clear the puck out of the crease.
The Ducks (18-23-7) went on the power play twice in the second period, but the Dallas penalty kill was up to the challenge both times.
"You don't like to end something like we've got going on a situation like that," Ducks coach Bruce Boudreau said. "You could tell early on that Lehtonen was really on his game and it was going to take something special (to beat him)."
At 13:36 of the second, Hiller stopped a shot by Dallas center Tom Wandell with a stellar glove save. Lehtonen delivered several key stops of his own in the second, including a stop on a long-range blast by Ryan Getzlaf at 10:24 and got a break at 16:38 when a shot by Teemu Selanne hit the post.
With 1:44 left, Selanne and Niklas Hagman executed a nice rush up the ice but Hagman's blast from dead center was denied by Lehtonen. The Stars goaltender also made a huge stop at the final whistle, denying an attempt by Koivu with his pads.
"They got a couple of good chances, but overall, especially in the third, we played pretty well," Lehtonen said. "They didn't get many shots and I think that was the big key."
Hiller stopped 15 of 16 shots in a losing effort. He left the ice with 1:44 remaining and while the Ducks were able to generate several chances with the extra attacker, they couldn't beat Lehtonen.
Dallas did not have a single power play in the vicory, the first time since the franchise moved to Dallas in 1993 that the Stars had won a game where they didn't go on the power play at least once.