Mitch Marner scored for Toronto, and Frederik Andersen finished with 26 saves.
Tied 1-1 in the third period, Stamkos threw a pass back into the slot to Killorn, who beat a down-and-out Andersen with a fluttering shot into the top of the net for his 18th goal of the season with 5:48 left.
The Maple Leafs pressed for the tie with Andersen on the bench, but Vasilevskiy stopped Patrick Marleau from in tight with his left pad on Torontos best chance before Kucherov sealed it with an empty-netter with 55 seconds left for his 40th of the season.
The game in front of a crowd of 19,400 at Scotiabank Arena was meaningless in the standings with both clubs locked in their spots — Tampa clinched the Presidents Trophy for the NHLs best regular-season record on March 18, while Toronto is cemented in the Atlantic Divisions No. 3 seed.
The Leafs are set to open their playoffs next week against Boston at TD Garden, the same building where they lost in Game 7 to the Bruins in last springs first round. The Lightning will meet the Eastern Conferences yet-to-be-determined second wild card.
Toronto opened the scoring at 4:41 of the first period when Marner disrupted a Lightning attack at the Maple Leafs blue line, got the puck back from Zach Hyman to create a 2-on-1 break the other way and beat Vasilevskiy between the pads for his 26th.
Andersen, who is looking to find his rhythm ahead of the playoffs after some shaky outings, made a terrific save on Mikhail Sergachev midway through the period, snapping his glove out to grab a quick shot off a feed from Kucherov.
Vasilevskiy then flashed some leather at the other end, getting a piece of Marleaus effort to keep his team within one through 20 minutes.
The Lightning got even at 5:37 of the second with a short-handed goal. Stamkos took a long pass from Ryan McDonagh before snapping a shot glove side on Andersen that the Toronto goalie could only get a piece of for the Tampa captains 44th.
Vasilevskiy stretched to deny Auston Matthews moments before that on a rebound off the end boards.
Anthony Cirelli rang a shot off the post behind Andersen with the teams playing 4-on-4 right off a neutral zone faceoff after Stamkos tying goal.
Andersen then stopped Stamkos, who limped to the bench right before his goal, on another blast and also thwarted Tyler Johnson late in the period.