The Jets played past regulation for the third straight game and fourth in the past five. They snapped a three-game losing streak.
Kari Lehtonen had 37 saves for Dallas, including four in the final minute of overtime.
The Jets were penalized for too many men on the ice with 24.6 seconds left in regulation, and Pavelec made a pad save on a point-blank shot from Benn just a few seconds after the faceoff.
The Stars had a 4-on-3 advantage for the first 1:35 of overtime, but the Jets had the two best scoring chances during that stretch. Bryan Little was stuffed by Lehtonen, and Zach Bogosian couldn't finish a play, trying to beat Lehtonen with a crossover on the goalie's glove side.
Stephane Robidas pulled Dallas even at 1-all at 6:36 of the third period when his shot from the point went through the legs of MacDermid and under Pavelec. The assists went to Lane MacDermid and Vernon Fiddler, who carried the puck into the zone and flipped a pass backward to Robidas.
Evander Kane opened the scoring at 3:28 of the second with a goal during a delayed penalty as an extra Winnipeg skater was joining the play. Kane settled the puck with his glove on the right wing and shot it past Lehtonen as the goalie was settling back in after jumping to make a pad save on a shot.
Tyler Seguin, who had a career-high four points when Dallas beat Winnipeg 4-1 for its only road win earlier this month, was held scoreless in regulation and overtime but had a team-high five shots.
Winnipeg just missed going up 2-0 in the opening seconds of the third period on a rush that ended with Dallas defenseman Jordie Benn sweeping the puck out of a wide open crease after a shot hit the post.
The Stars had a good chance to go in front with about 6 minutes left, but Seguin couldn't control the puck with Pavelec out of position.
Notes: The Winnipeg franchise had just one previous win in Dallas dating to its days in Atlanta. ... Stars defenseman Alex Goligoski played nearly 20 minutes after he was a healthy scratch in Thursday's 5-1 win over Calgary. Kevin Connauton, who replaced Goligoski against the Flames, was a scratch against the Jets. ... Winnipeg opened the second of 10 back-to-back sets this season. The Jets play at Colorado on Sunday night.