Stamkos scored his 20th goal to break a third-period tie, and the Tampa Bay Lightning rallied from an early two-goal deficit to beat the Maple Leafs 3-2 on Monday night.
"A pretty solid game by us all around," Stamkos said. "We dominated most of the play."
Stamkos gave the Lightning a 3-2 lead with his knee-high deflection of Matt Carle's shot with 8:55 to play. Tampa Bay also got goals from Ryan Callahan and Valtteri Filppula.
Mike Santorelli and Joffrey Lupul scored for the Maple Leafs, who gave up four third-period goals in a 6-4 loss Sunday at Florida. James Reimer started on consecutive days with Jonathan Bernier sidelined by flu-like symptoms and made 38 saves.
"Granted tonight, it's a back-to-back game," Maple Leafs captain Dion Phaneuf said. "They're sitting here waiting, and you could tell what team was fresher. But with saying that, that's part of playing in the National Hockey League. You've got to be able to play back-to-backs."
Toronto has lost five of six.
Santorelli put the Maple Leafs up 1-0 at 4:28 of the first when he lifted a shot from below the right circle over Ben Bishop, who stopped 21 shots.
Lupul made it 2-0 on Toronto's second shot, which came from the low slot off a pass by Tyler Bozak 7:47 into the first.
"That's not good," Bishop said. "You just kind of tell yourself that's enough, no more. I thought the guys did a good job of responding as far as peppering their goalie and getting some chances."
Callahan stopped a 13-game goal drought with a power-play goal he swatted into the net to cut Tampa Bay's deficit to 2-1 at 6:37 of the second. Filppula tied it 3:09 later.
Tampa Bay outshot the Maple Leafs 32-14 through two periods.
"I thought the way the game went, it was like we got scatterbrained for a bit in the second period," Toronto coach Randy Carlyle said. "Obviously, they had more shots than we did, and they controlled the puck more often. They were hungrier than we were, and they had better jump than we did, that's for sure."
Reimer stopped all 15 shots he faced in the first, and made a nifty glove save on Jonathan Drouin's shot from the left circle early in the second.
"My job is to stop them, whether there's 10 shots a night or 100 shots a night," Reimer said.
The Maple Leafs managed only four first-period shots, all in the first 9:34.
Lupul got Toronto's fifth shot 9 minutes into the second, a period in which Jake Gardiner hit the crossbar twice in the first 10 minutes and Bishop made a pad save on James van Riemsdyk's short-handed rebound backhander.
"It was nice to get rewarded," Stamkos said. "We stuck with it and didn't panic."
NOTES: Lupul has eight goals and 24 points in 20 games against the Lightning. ... Tampa Bay D Victor Hedman had two assists. ... Toronto RW Richard Panik sat out one day after getting hit in the head against Florida. ... Drouin played after sitting out one game due to flu-like symptoms. ... Lightning D Jason Garrison missed his third straight game with an undisclosed injury.