Stamkos forced overtime when he beat goalie James Reimer with a sharp-angled shot high on the short side.
"I just wanted to get a shot on net," Stamkos said. "Can I say I was going exactly for that top corner there? No, but you're just trying to put it on net and get some velocity on it, and it worked out."
Video: FLA@TBL: Point scores on first career SO attempt
Rookie defenseman Michael Matheson gave the Panthers a 3-2 lead with 4:08 remaining in the third on his first NHL goal. Greg McKegg carried the puck into the zone and around the net before he spotted Matheson at the left circle for a one-timer that beat goalie Ben Bishop through the five-hole.
"I saw that it was a delayed penalty, so I jumped into the rush," Matheson said. "McKegg] found me around the net and made a great pass."
Colton Sceviour and Trocheck also scored for the Panthers, who had won their first two games. Reimer made 25 saves in his first start for Florida.
Alex Killorn and Ondrej Palat also scored for the Lightning, who are undefeated through three games. Bishop made 28 saves.
[Video: FLA@TBL: Kucherov sets up Killorn for one-timer
Florida took a 1-0 lead at 2:38 in the second period on a shorthanded goal by Sceviour. Lightning defenseman Anton Stralman turned the puck over at the blue line, and the Panthers started a 2-on-1 the other way. Derek MacKenzie carried the puck to the right circle and fed the streaking Sceviour, who beat Bishop on the stick side.
Killorn tied it 1-1 at 6:18 of the second period on his third goal. Nikita Kucherov stripped Panthers defenseman Aaron Ekblad behind the net and set up Killorn with a one-timer in the slot that beat Reimer on the short side.
Palat gave the Lightning a 2-1 lead at 16:21 of the second when he took control of a loose puck and beat Reimer high. When Stamkos tried to beat Reimer with a wraparound, the Florida goalie got a stick on it, but he couldn't freeze the puck, and Palat put a shot into the top of the net from in close on the rebound.
The Panthers tied it 2-2 at 5:26 of the third period on Trocheck's second goal of the season. Reilly Smith tried a backdoor shot on Bishop, but the puck hit Lightning defenseman Jason Garrison's stick. Jussi Jokinen controlled it and centered to Trocheck, who scored high over Bishop.
Video: FLA@TBL: Trocheck chips home goal to tie game in 3rd