The game had a little bit of everything: 11 combined power plays, a shorthanded goal and two go-ahead goals that were overturned.
With the victory, Tampa Bay pulls within five points of the Leafs for second place in the Atlantic Division.
It'll be another division challenge for the Lightning when they resume the homestand on Tuesday, as the Red Wings make their first visit of the season.
Scoring Summary
1st Period
No Scoring
2nd Period
TOR 1, TBL 0
5:18 Mitch Marner (9) - David Kampf - SHG
The Lightning's third power play chance of the night got off to a dreadful start with Tampa Bay turning the puck over deep in their own zone. Mikhail Sergachev left a drop feed that was easily intercepted by Mitch Marner. After missing high with the initial shot, David Kampf retrieved the loose puck and set up Marner again for the shorthanded goal.
TOR 1, TBL 1
7:40 Vladislav Namestnikov (1) - Anthony Cirelli, Erik Cernak
Erik Cernak's shot from the point was inadvertently blocked by Anthony Cirelli in the slot. Vladislav Namestnikov quickly pounced on the loose puck and fired it past Matt Murray for his first goal of the season to draw the Bolts level.
TOR 2, TBL 1
16:50 William Nylander (14) - Auston Matthews, Michael Bunting
Momentum swung back in Toronto's favor in a big way late in the period. Just 28 seconds after Tampa Bay had a go-ahead goal wiped off the board by a successful offside challenge from the Leafs, William Nylander swept home a backhander to put them back in front, 2-1.
3rd Period
TOR 2, TBL 2
1:51 Nikita Kucherov (11) - Steven Stamkos, Corey Perry - PPG
Tampa Bay took advantage of a 4-on-3 power play early in the third period and tied the game at two on a Nikita Kucherov wrist shot from the top of the right circle.
TBL 3, TOR 2
4:34 Ross Colton (6) - Mikhail Sergachev, Corey Perry - PPG
A scramble in front of the Toronto net pulled Murray out of position. The Bolts quickly worked the puck back to Mikhail Sergachev at the point and he teed up Ross Colton for a one-timer from a sharp angle that give Tampa Bay their first lead of the night.
TBL 3, TOR 3
11:55 Mitch Marner (10) - Unassisted - PPG
Marner's second goal of the night came on a Toronto power play and tied the game at three. The Bolts were left even more shorthanded on the play when Nick Paul broke his stick, creating extra time and space for Marner to fire home a shot from the high slot.
Overtime
0:33 Alex Killorn (8) - Anthony Cirelli
It didn't take long to settle things in overtime, with Alex Killorn wiring home the game-winner from the right circle just 33 seconds into the extra session.