Jason Spezza scored in the shootout, and the Stars snapped a three-game losing streak with a 2-1 victory over the Rangers.
Kari Lehtonen made 24 saves for Dallas in the opener of its four-game East Coast road trip against the Metropolitan Division. It was Lehtonen's 299th career NHL victory.
Dallas outshot New York 45-25, but Pavelec kept the Rangers in the game with an outstanding performance in goal.
The Stars had a 1-0 lead before Rick Nash tied it for the Rangers when he tipped in Brady Skjei's wrist shot with 3:41 left in regulation. Nash made contact with Lehtonen but the goalie was well outside the blue paint. Hitchcock challenged the play, but the referees stayed with the original call.
Julius Honka put Dallas in front when he drove a slap shot past Pavelec at 6:30 of the second period for his first of the season. The 2014 first-round pick rejoined the lineup after sitting for the previous three games.