Esa Lindell scored for the Stars (18-15-2), who are 4-12-1 on the road this season and lost 7-1 at the Florida Panthers on Friday. Anton Khudobin made 26 saves in his first start since Nov. 18.
"[Khudobin] was great, he gave us a chance to get a point out of a game," Dallas coach Rick Bowness said. "I mean, we're not going to win anything on the road until we get more than one goal. Anton did his job and made some big saves when he had to."
Ross Colton scored a tiebreaking third-period goal for the Lightning (26-9-5), who have won five of six. Andrei Vasilevskiy made 19 saves.
"It's a good test, especially when a team has given up a few like they did the other night, you knew they were going to push," Tampa Bay coach Jon Cooper said. "And they did. [We] defended really well and waited for their breaks, and if we did break down, 'Vasy' was there."