Talbot then stopped Jason Robertson on a breakaway with a left-pad save at 16:45.
Dallas appeared to open the scoring in the final seconds of the second, but video review confirmed the puck did not cross the goal line before time ran out.
During a 3-1 win over the Blue Jackets in Dallas on Saturday, the Stars scored in the final second of the first period and into an empty net at 19:59 of the third.
“We played them twice here in the last week and they've played some good hockey,” Dallas coach Glen Gulutzan said. “So, it was a good hockey game, tight-checking and it was back to our identity.”
The Stars finally broke through when Rantanen scored for the third straight game for a 1-0 lead at 6:27 of the third period.
Wyatt Johnston pounced on a Ivan Provorov turnover and forced a save by Talbot. The rebound went to the right of the net where Rantanen collected it and calmly waited for an opening at the near post.
“We were turning some pucks over, especially in the second period,” said Rantanen, who was playing his 100th game with Dallas. “We should have had a goal or two probably there but forecheck was good. Our 'D' was doing a good job joining the rush, getting some chances from there and extending the O-zone time, so that was good.”
Johnson was happy to see Werenski end his goalless streak.
“I'm not sure how much it was bothering him,” Johnson said. “He cares first about the team winning game so there's games we lost where he probably felt like he could have scored, I'm sure that that weighed on him a bit.”
NOTES: Werenski has seven points (one goal, six assists) in a five-game point streak. … Johnson had an assist to extend his point streak to six games (three goals, six assists). … Johnston has six points (one goal, five assists) in a four-game streak. ... Rantanen has five points (three goals, two assists) in a four-game streak. His 114 points (36 goals, 78 assists) are the third-most through a player’s first 100 games with the franchise, behind Dino Ciccarelli (127) and Neal Broten (120). ... Stars defenseman Miro Heiskanen did not play after sustaining an upper-body injury in a 6-5 win at the Washington Capitals on Tuesday. Gulutzan said Heiskanen may be available Saturday against the San Jose Sharks. … Dallas was without forward Sam Steel, who was unavailable for personal reasons.