Alexei Ponikarovsky and Jeff O'Neill also scored for the Leafs, who had been 0-6-1 since a Nov. 24 win, and Andrew Raycroft came off the bench early in the second period to supply solid relief goaltending.
Nikita Alexeev, Vincent Lecavalier, Brad Richards and Martin St. Louis scored for the Lightning.
Ponikarovsky opened the scoring with a power-play goal at 3:28. Tomas Kaberle sent a cross-ice pass into the circle to the left of goaltender Johan Holmqvist and Ponikarovsky fired a low wrist shot for his ninth goal of the season. Doug Janik was in the penalty box for hooking Tucker.
Alexeev tied it with his ninth at 7:32. Lecavalier fed the six-foot-six Russian in the circle to the right of Jean-Sebastien Aubin. The puck entered the net in the top short-side corner as Aubin went into a crouch.
Lecavalier put Tampa Bay up 2-1 with a power-play goal at 12:29. Mike Peca was off for boarding Paul Ranger. Dan Boyle fed a pass into the circle to the left of Aubin and Lecavalier banged in a slap shot for his 18th goal. The puck eluded Aubin on his stick side. It was a shot many goalies would have stopped.
It wasn't looking good for the Leafs: Tampa Bay entered the game 7-1-0 when leading after one period, and Toronto was 0-7-1 when trailing after one.
Richards made it 3-1 with his 12th goal just 24 seconds into the second period. Brian McCabe got only a piece of the puck behind his net when he tried to shoot it around the boards and it bounced to St. Louis, who quickly relayed it out front to Richards for a redirect into the top of the net.
Aubin was pulled, and he let coach Paul Maurice know he wasn't happy about it when he got to the bench. He'd allowed three goals on nine shots. Raycroft took over.
Kilger made it 3-2 at 12:55. Holmqvist was sprawled in his crease after stopping a Tucker slap shot when Kilger lifted the rebound into the open side of the net.
Kilger tied it 3-3 at 19:31 when he pushed in a Mike Peca pass on a rare 2-on-0 rush for his sixth goal of the season.
For the first time in a long time, the Leafs clawed their way back into a game after blowing a lead, jumping ahead 4-3 when Tucker deflected in a Mats Sundin shot at 3:37 of the third period. It was Tucker's team-leading 18th goal, and his 13th with the man advantage. Ryan Craig was in the penalty box for tripping Bates Battaglia.
O'Neill put in a rebound for his ninth with Holmqvist down at 10:55.
With Kilger off for hooking, St. Louis slid a bad-angle shot from the side of the net in off Raycroft's leg pad on a power play at 16:16 to set up a tense finish.
Raycroft stopped all but one of the 17 shots he faced.
Toronto was 2-for-4 and Tampa Bay 2-for-5 on power plays. Tampa Bay had a 26-25 edge in shots on goal.
Notes: Former Leafs coach Pat Burns and former GM Cliff Fletcher were in the crowd of 19,462 . . . Lecavalier has scored eight goals in his last seven games and is on a seven-game points streak (8-6-14) . . . Carlo Colaiacovo got into his first game of the season in place of Brendan Bell . . . C Nik Antropov missed a third straight game with a sore ankle. Fans cheered the pre-game announcement of the lineup scratch . . . In their previous 31 games, the Leafs outscored opponents 33-27 in first periods and 36-31 in second periods, but they were outscored 42-23 in third periods . . . Toronto entered the game ranked eighth in the league on power plays and 22nd in penalty killing . . . The Leafs are at Carolina on Friday three years to the day after Paul Maurice was fired by the Hurricanes . . . Most career points as a Maple Leaf: Darryl Sittler 916, Dave Keon 858, Sundin 856 . . . Tampa Bay forward Rob DiMaio, who suffered a concussion Sept. 26, still hasn't been able to resume his career.