Tavares skated out from behind the net sent a spinning shot toward the net, where it deflected in off the skate of Lightning defenseman Darren Raddysh's skate.
"I got the puck up high and interchanged with [Mitchell Marner], and I thought most of the coverage would go to him," Tavares said. "But they read it well and I just kept the puck in. ... With the space that I had and knowing [Morgan Rielly] went to the net, I said let's throw it there and see what happens."
The Maple Leafs, who won all three games at Amalie Arena in overtime, will play the winner of the series between the Boston Bruins and Florida Panthers, which concludes Sunday with Game 7 in Boston.
"It's been a long time coming, a long time coming for a lot of players in our room, long time coming for myself, long time coming for Leafs Nation. ... It's a big deal," Toronto coach Sheldon Keefe said. "You see that puck find its way in the net and it's just an incredible moment. Playoff hockey is incredible. This whole night was incredible."