The Sharks slowed down Dallas' playoff push, although the Stars have gone 5-1-2 in their last eight contests.
San Jose's Martin Havlat broke a scoreless tie with 1:54 to go in the middle period and Dallas tied it on a goal from Valeri Nichushkin 6:27 into the third.
The goal by Wingles was his 11th of the year and came off Kari Lehtonen, who stopped 19 shots.
Alex Stalock picked up the win, also making 19 saves. Dallas had been trying to complete a perfect three-game road trip.