"I just didn't want to give up 60," said Scrivens, the Leafs' goalie. "It would be on the highlights all summer."
Stamkos is trying to become the NHL's first 60-goal scorer since Washington's Alexander Ovechkin had 65 in the 2007-08 season, and only the second player to reach that mark in the past 15 years.
"He's a team player and he cares about the right things for the right reasons," said coach Guy Boucher. "Whether it's 59 or 60, it doesn't make a difference in the quality of the player."
Stamkos badly wanted to get the job done in his hometown -- "Oh yeah, it'd be special," he said before the game -- but heads to Winnipeg instead needing a goal in Tampa's final game on Saturday.
His coach was clearly trying to help him along. Stamkos received a team-high 25:08 of ice time and matched his season-high with eight shots on goal.
"You could see definitely that their hockey club is trying to push the puck in his direction," Leafs coach Randy Carlyle said. "We were fortunate I think tonight to only hold him to one. He had lots of chances."
Martin St. Louis added a goal for the Lightning.
Stamkos appeared to be headed for his league-leading 13th game-winner of the season after sneaking behind the Toronto defense and converting a perfect pass from Bruno Gervais at 8:48 of the third period to make it 2-1. But Gardiner tied it up with less than three minutes to play in regulation by banking the puck in off a defender.
There was very little atmosphere for Toronto's final home game of the season. With the team long out of playoff contention and the Blue Jays' marathon opener in Cleveland stretching into the Leafs' game time, there were several clusters of empty seats at Air Canada Centre.
It was just the team's second win on home ice in the last two months -- an ugly 2-8-3 stretch that contributed to a seventh consecutive season outside the playoffs.
But the players took some solace in being able to leave the ice to cheers while saluting the fans with sticks raised high.
"We've got great fans," Phaneuf said. "We struggled at home for a while, no one was happy about it. We have not been playing the way that we want to play.
"But we wanted to finish our year off, our last game at home in front of our fans, the way we [did]."
St. Louis opened the scoring for Tampa Bay with a shot that caromed off some bodies and past Ben Scrivens 5:49 of the first period. Stamkos was standing at the edge of the crease but didn't pick up a point on the play.
It took less than a minute for the Leafs to tie it up, with Connolly getting a beautiful pass from Gardiner and having a wide open net to shoot at.
Stamkos truly began establishing his presence during a second period where he was credited with six shots. Scrivens stopped him with a toe save early on before getting a blocker on another good shot through traffic.
At the other end, Roloson did his part to keep the game close.
- Leafs F Joffrey Lupul took the morning skate -- his first since separating a shoulder March 6 -- but won't play again for Toronto this season.
- Former Leafs goalie Johnny Bower received a loud ovation when he was shown on the scoreboard.
- Stamkos has three goals in eight career games at Air Canada Centre.