With the teams trading chances back in forth during an entertaining extra session, Tyler Bozak intercepted a pass and broke in on a 2-on-1, deked around Vincent Lecavalier and slipped the puck to an open Kessel, who easily beat Mike Smith.
Bozak also scored in regulation, while fellow rookie Viktor Stahlberg had two goals to help the Maple Leafs (22-33-12) win for the third time in four games. Luca Caputi, another rookie, added two assists.
Steven Stamkos, extending his points streak to 18 games with his 42nd goal of the season, Kurtis Foster and Steve Downie replied for the Lightning (27-27-12), who lost for the seventh time in eight games.
Tampa Bay — fighting for the final playoff spots in the Eastern Conference with Montreal, Boston, the Rangers and Atlanta — struggled to contain the Leafs' kids all night and eventually paid for it.
Bozak put the Leafs ahead 3-2 just 3:37 into the third when he picked up a loose puck to Smith's right and fired it over the prone goalie.
But Downie fired home a rebound past Jean-Sebastien Giguere just 1:13 later, setting up the exciting finish.
NOTES: D Garnet Exelby and F Frederik Sjostrom were scratched for the Maple Leafs, while F Todd Fedoruk, tough guy Zenon Konopka and D Matt Smaby sat out for the Lightning. ... Leafs D Luke Schenn twice drilled Lightning F Alex Tanguay.
(This version CORRECTS Maple Leafs 4, Lightning 3, OT. corrects Tampa Bay's record.)