Paul scored in the first to put the Lightning in front and netted the game-winner at 16:32 of the second period.
Vasilevskiy played brilliantly all night, but was at his best in the third period. Vasilevskiy stopped all 17 shots the Leafs threw his way in the third to backstop the victory.
Next up for the Bolts is a Second Round matchup against the Presidents' Trophy-winning Panthers. Tampa Bay will begin that series on the road for Games 1 and 2.
Scoring Summary
1st Period
TBL 1, TOR 0
18:24 Nick Paul (1) - Ross Colton
Immediately after Mark Giordano's shot on 2-on-1 was deflected wide, the Bolts quickly went the opposite direction on an odd man rush. Ross Colton's initial one-timer was partially blocked but still got through to Jack Campbell, forcing him to make an awkward pad stop. Nick Paul continued to drive to the net, beating Morgan Rielly to the rebound and steering it home for the game-opening tally.
2nd Period
TBL 1, TOR 1
13:25 Morgan Rielly (3) - Auston Matthews, Mitch Marner
Morgan Rielly jumped up on the rush to score the game-tying goal at 13:25 of the second period. The Leafs worked the puck across the middle of the ice to Rielly on the right wing, and he snapped a shot upstairs on Andrei Vasilevskiy to level the game at one.
TBL 2, TOR 1
16:32 Nick Paul (2) - Unassisted
While driving down the far wall, Alex Killorn collided with Jake Muzzin, wiping him out of the play and opening space for Paul to pounce on the puck inside the blue line. Paul stick-handled his way to the slot and beat Campbell to put the Bolts back in front late in the second.
3rd Period
No Scoring