"He bought lunch today, so I think he's going to have to do that again," Benn said.
Tampa Bay dominated early in overtime, with the first four shots on goal. But then Benn took the puck away in the Dallas end, bounced off a hit, passed to Cody Eakin and took a return drop pass before sending a shot past Lightning goalie Andrei Vasilevskiy for his 20th goal.
"Just for the three guys to get up ice and make the play, I thought they made a good play," Stars coach Lindy Ruff said, "and Jamie hit a shot."
Dallas goalie Kari Lehtonen held Tampa Bay scoreless for the final 34 minutes, with 15 of his 34 saves coming in the third period and overtime.
"We did everything we could in overtime," Lightning coach Jon Cooper said. "We couldn't put (the puck) behind their guy. They got their one chance, and it had to be on one of the best player in the league's stick."
The Stars won for the first time this season when trailing after two periods. They are 1-22-2 in those situations, and 3-9 in overtime.
Roussel, popular in Dallas primarily because he leads the NHL with 115 penalty minutes, scored the team's first three goals as the Stars came back from deficits of 2-0 and 3-2. His first two came six minutes apart in the first period, and his third tied the game 3-all at 4:40 of the third.
"It was awesome. It was fun to watch," Benn said. "All that hard work paid off."
Tyler Seguin assisted on all three of Roussel's goals.
"It feels pretty good," Roussel said. "Our main focus before the game was we had to work hard, and everything's going to come to us and basically that's what happened."
Dallas, last in the NHL in penalty killing, allowed goals on both Lightning power plays.
Both teams are fighting to get into playoff position. The Lightning entered six points and six teams removed from the Eastern Conference's second wild card. Dallas was seven points and three teams away from a postseason berth.
Roussel's first goal came off a backhand pass from Dan Hamhuis that Roussel redirected past Vasilevskiy, who finished with 24 saves.
At 18:50 of the first period, Seguin passed from the slot to Roussel on the left.
On Roussel's third goal, Seguin passed from behind the goal line to his teammate in the middle of the left faceoff circle.
The Stars have given up at least one power-play goal in 19 of their past 23 games. ... Hedman, one of the NHL's top defensemen, has four three-point games this season. He has had three regular-season games with two goals in his eight NHL seasons, most recently on Nov. 27, 2013, vs. Philadelphia. ... Roussel has scored multiple goals three times in his five seasons, including twice in 2013-14. ... In his last 11 games against Tampa Bay, Seguin has 15 points (five goals, 10 assists). ... Johnson missed the Lightning's previous two games because of a lower-body injury. ... Vasilevskiy had won his first two games against the Stars. ... Dallas RW Adam Cracknell left in the third period favoring his right leg after Johnson checked him into the boards. "It looks fairly serious," Ruff said. . Stars play-by-play broadcaster Dave Strader called his first game this season after undergoing cancer treatment. "This win is really for him," Roussel said. "He's going to be our good-luck charm."
Lightning: Travel to Colorado for the last of four straight road games on Sunday. This is the first of five back-to-back road games remaining on Tampa Bay's schedule.
Stars: After a five-day break for their bye week, they'll play the second of five games in a row at home on Friday against Arizona.