For Garrison, an undrafted player out of British Columbia, it was his fourth goal of the season and the third game-winner. Garrison took a pass from Mike Santorelli and let loose a one-timer from in close that beat Mike Smith.
Garrison previously scored decisive goals against Buffalo and San Jose.
Vincent Lecavalier and Simon Gagne scored late in the third period for Tampa Bay to erase a 3-1 deficit, but Garrison's fourth goal of the season gave the Panthers their fourth win in five games against the Lightning this season.
It was also the seventh of the last 11 meetings between the Southeast Division rivals that has come down to one goal, with four of the last six extended to a shootout.
"They've all gone to one-goal games and we've had a successful road against them," Garrison said. "Obviously, we see them a lot throughout the year and it's good for the fans...and it's definitely a good one out there on the ice."
Ryan Carter and Niclas Bergfors each scored their first goals for Florida as the Panthers gained a two-goal cushion earlier in the third period.
Carter, acquired in the Cory Stillman trade with Carolina; and Bergfors, dealt from Atlanta in the Radek Dvorak deal late last month, scored 2:56 apart.
Bergfors was in the box for high sticking when Tampa Bay came through with the equalizer on Gagne's shot that first hit the post and then deflected into the net off Scott Clemmensen with 2:05 left in regulation.
"We nearly gave them the game but I'm glad we got the win," Bergfors said.
The loss sent the Lightning, who are battling with Washington for the top spot in the Southeast Division, to their sixth loss in seven games.
"The only thing you can ask of this team is to play hard and keep doing what they're doing. Obviously we all have to do more," Tampa Bay winger Martin St. Louis said.
Carter took possession deep in the Tampa Bay end, weaved down the center of the ice and found the five-hole against Smith to make it 2-1 before Bergfors tucked one past Smith for the two-goal advantage.
"That's a talented team with guys that can score so to give up a two-goal lead like that and not lose your marbles, stay in the game and be able to finish it, that says a lot about the guys in here right now," Carter said. Tampa Bay cut the deficit to 3-2 when Lecavalier scored his 17th goal with Garrison serving a double-minor for high sticking midway through the period.
Clemmensen, getting the start over Tomas Vokoun, faced a barrage late as the Lightning was able to force the overtime session. Tampa Bay outshot the Panthers, 38-27.
"All the top teams are living the same thing. Today we fought all game and made it happen but it took everything he had," Lightning coach Guy Boucher said.
David Booth, who entered with 3 goals and an assist against Tampa Bay this season, gave Florida the early lead with his team-leading 21st of the season at 4:33 of the second period. Booth took a pass from Mike Weaver just inside the blue line and beat Smith to the glove side, giving him goals in four of his last five games.
The Lightning's Steven Stamkos provided the equalizer less than 10 minutes later after Florida had escaped a 5-on-3 disadvantage for 33 seconds.
Just seconds after Booth left the penalty box for high sticking, Stamkos blasted a one-timer past Clemmensen from the top of the left circle for the power-play goal at 14:10. Stamkos, who has scored 23 goals on the road this season (20 at home), extended his points streak to four games. He is 2-3-5 over that stretch.
The Panthers were unable to convert on four power-play opportunities over the first two periods, while Florida allowed three power-play goals for the first time this season.
"We did a lot of good things and then turned around and shot ourselves in the foot a few times, but I think the result was the right one," Florida coach Peter DeBoer said.
Material from wire services and team media was used in this report.
|David Booth (21) Wrist shot - ASST: Mike Weaver (10), Keaton Ellerby (9)|
1 - 0 FLA
|PPG - Steven Stamkos (43) Slapshot - ASST: Martin St. Louis (54), Simon Gagne (13)|
1 - 1 Tie
|Ryan Carter (2) Wrist shot - ASST: Dmitry Kulikov (17), Mike Santorelli (18)|
2 - 1 FLA
|Niclas Bergfors (12) Tip-in - ASST: Jason Garrison (11), Stephen Weiss (27)|
3 - 1 FLA
|PPG - Vincent Lecavalier (17) Tip-in - ASST: Martin St. Louis (55), Simon Gagne (14)|
3 - 2 FLA
|PPG - Simon Gagne (11) Wrap-around - ASST: Vincent Lecavalier (22), Steven Stamkos (41)|
3 - 3 Tie
|Jason Garrison (4) Backhand shot - ASST: Mike Santorelli (19), Marty Reasoner (15)|
4 - 3 FLA
|Nate Thompson Roughing against Dmitry Kulikov|
|Victor Hedman Hooking against Sergei Samsonov|
|Marty Reasoner Tripping against Adam Hall|
|Michal Repik Too many men/ice - bench|
|David Booth Hi-sticking against Dominic Moore|
|Jason Garrison Hooking against Vincent Lecavalier|
|Dana Tyrell Holding the stick against Clay Wilson|
|Brett Clark Interference against David Booth|
|Jason Garrison Hi stick - double minor against Steven Stamkos|
|Bill Thomas Too many men/ice - bench|
|Niclas Bergfors Hi-sticking against Martin St. Louis|