"[Lundqvist] gave us a chance to win, and that's what you want from your goaltender," coach Alain Vigneault said.
Hanzal scored on the power play at 4:05 of the third when he tipped a Julius Honka shot from the point to make it 2-1. It was Hanzal's first game back after missing five with a lower-body injury.
"I feel OK," Hanzal said. "It's always hard when you get back when you miss a long time. It's hard to get in game tempo. It took me a couple shifts, but after that I felt pretty good. Scoring the goal, it was lucky on the tip and went in."
Hanzal won eight of 11 face-offs and was a key part of the Stars penalty kill, which went 3-for-3.
"He just manages the game so well, he's a real good player, and we've missed him," Stars coach Ken Hitchcock said. "We've missed his presence, he's a real good pro, and I guess we're hoping that he stays healthy. He came through the game fine, and that's a good sign. And a healthy Martin Hanzal makes us a lot different hockey club, and very difficult to play against."
After Vinni Lettieri stole the puck from Dallas forward Devin Shore in the neutral zone, Desharnais gave New York a 1-0 lead at 17:55 of the first period when he scored on the rebound of a Lettieri shot.