Stamkos was just 5 for 27 in the shootout coming into the game, but he made some nice moves to slip the puck past Jacob Markstrom on his left side for the deciding goal in Tampa Bay's fourth slot.
''It's something that I struggled with in the past but practice does help with certain moves,'' Stamkos said. ''I probably wasn't going to be in the first three but I was glad to go in there and help the team win in any situation. It's nice to see one go in and even nicer to help your team win in that situation.''
Stamkos, Radko Gudas, and Martin St. Louis scored in regulation for Tampa Bay, which has won five of six. Anders Lindback stopped 29 shots and turned aside three of four Florida shooters in the tiebreaker. Stamkos also had an assist.
Lindback got his first win of the season.
''We got another two points. Obviously for me coming in and winning a game, it's nice,'' said Lindback, who started in the second half of back-to-back games in place of Ben Bishop.
''He stopped a couple of their guys in the shootout,'' Lightning coach Jon Cooper said. ''That's where you need your goalie to stand up and win a game. He did that for us tonight.''
Brad Boyes, Nick Bjugstad and Shawn Matthias scored, and Markstrom made 25 saves for Florida. Boyes also had a shootout goal. Jonathan Huberdeau, Aleksander Barkov, and Dmitry Kulikov all missed.
The Panthers lost for the fifth time in seven games, including two shootouts.
''Unfortunately, we end up on the wrong end of these (shootouts) right now, but there's guys that are pushing hard and that's what we have to keep doing,'' Panthers coach Kevin Dineen said.
Florida rallied from a 3-1 deficit in the third period.
The Panthers closed to 3-2 on Bjugstad's goal at 5:39 when he tipped in Scottie Upshall's shot from the point.
Florida tied it when Boyes grabbed an errant puck and backhanded it under Lindback's pads from in front at 8:51. Boyes leads the Panthers with five goals, but this was his first in seven games.
Tampa Bay stretched its lead to 3-1 during a power play in the second period. Gudas took a wrist shot from just inside the blue line that deflected off Florida's Mike Weaver and got past Markstrom at 9:58.
Gudas got a game misconduct at 12:51 of the third when he slashed at the boards in front of the Panthers' bench after being squirted with water by Upshall, who received an unsportsmanlike conduct call.
Florida closed to 2-1 on Matthias' first goal of the season. Matthias grabbed a puck in traffic in front of the crease and slipped it behind Lindback at 13:48 of the first. It was Matthias' first goal in 23 games, dating to last season.
''It's tough going down 2-0 early like that, but we played really hard and battled back,'' Matthias said. ''It's tough to have the final outcome happen.''
The Lightning scored two goals on their first three shots, including on just 41 seconds into the game. Stamkos passed from the top of the right circle to St. Louis, who poked in the puck from in front. St. Louis has scored in three straight games.
Stamkos made it 2-0 at 4:35. Markstrom blocked a shot by Ryan Malone, but the long rebound went out to Stamkos in the right circle for a slap shot.
The Lightning improved to 8-3.
''It's probably the quietest 8-3 record in the league and we like it that way,'' Stamkos said.
NOTES: Stamkos leads the Lightning with eight goals and 17 points. ... St. Louis has seven goals and 14 points in his past 10 games. ... Matthias' previous goal was March 30 against New Jersey. ... Florida LW Tomas Fleischmann was scratched due to illness.