"It feels like he's locked in all the time, to be honest with you," Lightning forward Steven Stamkos said. "That's how amazing he is. We just try to make it as easy for him as we can, but he's the best goalie in the world for a reason, and he's showing it."
Anthony Cirelli and Stamkos each had a goal and an assist for Tampa Bay (14-4-1), which has won four straight.
Anton Khudobin allowed five goals on 17 shots and was pulled 1:07 into the third period for Dallas (6-6-4), which is 2-5-3 in its past 10 games. Jake Oettinger made five saves in relief.
"We'll turn it around," Stars coach Rick Bowness said. "We've had a bad 10-game segment. We've lost some games we should've won. We certainly didn't deserve to win tonight. When you lose games you played well enough to win, it's going to bite you."
The Lightning defeated the Stars in the Cup Final, with Vasilevskiy making 22 saves in a 2-0 clinching win in Game 6 on Sept. 28.
"It's certainly not the feeling that it was the last time we played them," Stamkos said. "It's a different year. As much as people want to make a storyline about it, it's a game, and once both teams get on the ice they want to win."