William Nylander had a goal and an assist for the Maple Leafs (33-23-8), who lost their previous game to emergency goalie David Ayres and the Carolina Hurricanes on Saturday. Frederik Andersen made 26 saves to keep Toronto two points ahead of the Florida Panthers for third place in the Atlantic Division.
"We've scored a lot of goals all year, I'm not too concerned about us finding ways to put the puck in the net," Tavares said. "We just have to play to our capabilities and have that consistency."
WATCH: [All Maple Leafs vs. Lightning highlights]
Andrei Vasilevskiy made 19 saves for the Lightning (40-18-5), who lost at home for the first time in 12 games and have lost three straight for the first time this season. Tampa Bay is second in the Atlantic Division, five points behind the Boston Bruins.
"We didn't play poorly 5-on-5, we didn't give them anything," Lightning coach Jon Cooper said. "It was a total special-teams game. When you lose a hockey game and the losing team's players are plus and the [winning] team's players are all minuses, you know what decided that game."
Tavares' second of the game gave the Maple Leafs a 3-2 lead at 12:25 of the second period. Nylander made it 4-2 with power-play goal at 14:21 when he went between his legs and beat Vasilevskiy to the far post.
"That's pretty sweet; I didn't know he went in between the legs at first, I saw it here after," Maple Leafs defenseman Tyson Barrie said. "He's been scoring big goals for us all year and obviously that was a beauty tonight."