Stamkos scored two goals -- giving him an NHL-best 47 -- including the winner 2:41 into overtime as the Lightning beat the Carolina Hurricanes 4-3 on Saturday night.
Teddy Purcell extended his career-best point streak to nine games with a power-play goal in the third, and added an assist on Stamkos' game-winner. Tim Wallace netted the first goal of his career, and Mathieu Garon had 25 saves in the win.
"That was a big character win for our team," Stamkos said. "We got some breaks with a 5-on-3 when we were able to tie it, and in overtime. Finally, we were able to take advantage of some power plays. We may have not played our best game, but we found a way to win, and that's what matters."
Tampa Bay won in overtime for the second straight night after beating the New York Rangers at home on Friday.
"These guys are doing the impossible, so no matter how we do it doesn't make a difference," Lightning coach Guy Boucher said. "We find ways, and we'll take it."
Anthony Stewart had two goals in his first multipoint game for Carolina, and Jussi Jokinen also scored for the Hurricanes. Carolina captain Eric Staal, who had two assists, extended his NHL-best point streak to 11 games and his assist streak to 10.
Staal matched the marks he and Cory Stillman share for the club's longest scoring streaks since the team relocated from Hartford in 1997.
Cam Ward, playing in his 400th NHL game, stopped 19 shots in the loss.
The winning goal was scored while Brandon Sutter was in the penalty box following a roughing call at 1:05. Sutter and Stamkos got tangled up on a rush before Sutter collided with Garon.
"We played start to finish a playoff-style game," Hurricanes coach Kirk Muller said. "Our guys are competing and playing at a high level. I'm really happy with the performance. Stamkos has got the ability to score, and I thought we limited him really well here. He's a world-class player and he can capitalize on it."
Wallace gave Tampa Bay the lead at 5:58 with his first goal in 58 games. Wallace was in his third game with Tampa Bay after being claimed off waivers from the New York Islanders.
Stewart scored the tying goal from Staal at 5:23 of the second, and goals from Jokinen and Stewart made it 3-1 before Stamkos scored on a rush at 18:00.
Purcell connected to tie it during a 5-on-3 power play at 7:24 of the third.
It was the 100th game between the teams. ... The Hurricanes went 2-1-3 on their six-game homestand. . RW Chad LaRose played in his first game for Carolina after missing seven because of an undisclosed upper body injury. . D Mike Commodore, playing his second game for the Lightning, was a member of Carolina's 2006 Stanley Cup championship team. ... Jokinen played with the Lightning from 2007-09. ... Carolina RW Tuomo Ruutu (eighth game, upper body) and RW Patrick Dwyer (third game, lower body) sat out. ... Tampa Bay D Victor Hedman (upper body) missed his fourth game.