Toronto picked up two crucial points against one of the teams battling for playoff positions in the tight Eastern Conference race.
The night began with Tampa Bay, Toronto, Montreal, the New York Rangers, Detroit, Columbus and Philadelphia holding down the third through ninth positions in the conference standings and all of them separated by just seven points.
After Ondrej Palat scored for the Lightning, Tyler Bozak added an empty-net goal with 2:52 remaining.
Jonathan Bernier recorded 31 saves for the Maple Leafs. Ben Bishop started in goal for Tampa Bay, but left after two periods with an upper body injury. Bishop was replaced by Cedrick Desjardins, who allowed the two key third-period goals on 11 shots.