Alexander Barabanov, Logan Couture, and Tomas Hertl each had a goal and an assist, and James Reimer made 25 saves for San Jose (4-9-3), which went 0-2-3 over its previous five games.
"I think we're slowly learning what it takes to win hockey games," Sharks coach David Quinn said. "I thought our breakouts were clean; I thought we caused a lot of turnovers. We went hard to the net in the [offensive] zone.
"There were a lot of good things in our game, and we took a step forward in learning how to win a game. It's going to take a little time, we're still fragile from the last two weeks and the losing we've done, and the way we've done it. But we took a step forward tonight."
Jamie Benn scored twice, and Roope Hintz scored for the Stars (8-4-1). Jake Oettinger made 13 saves in his return from a lower-body injury sustained against the New York Islanders on Oct. 29.
"They only had 20 shots," Oettinger said. "We scored four goals, and when you score four goals, you expect to win. I definitely could have made another save or two and at least helped us get to overtime. I know I have [to be] better, and just [have] to do it next game."