Toronto ended a five-game skid.
The Maple Leafs scored three times in the middle period to take a 4-0 lead and survived two late goals surrendered by James Reimer, who got the win by stopping 26 shots.
Mathieu Garon gave up three goals on 13 shots in just over 27 minutes before being removed for Anders Lindback.
Tampa Bay came up with goals from Radko Gudas and Cory Conacher in the third period, but had a two-game winning streak snapped.
Wisconsin business offering 'therapeutic cuddling' forced to close
Police: Sword-wielding man demanded free tacos