Stamkos had two goals and an assist, Garon made 24 saves and Tampa Bay beat the Panthers 5-1 on Saturday night.
"We slowed them down a little bit," St. Louis said.
Garon stopped four shots by former Lightning left wing Sean Bergenheim during the opening period. The goalie turned aside 23 shots in Friday's victory over the Panthers.
Tampa Bay took control during the second when goals by Pyatt, Stamkos and Malone made it 4-0. Stamkos got his second of the game and 14th of the season in the final minute of play.
Stamkos scored Friday's winner in overtime.
The Southeast Division-leading Panthers, who went 0 for 6 on the power play, got a late third-period goal from Shawn Matthias. Florida had won three in a row before the consecutive losses to Tampa Bay.
"We got outplayed and the score shows how the game played out," Florida coach Kevin Dineen said. "Goaltending wasn't an issue, it was overall defensive play and a real lack of will. We need to get back to the way we've been successful, and we didn't do that for the last four or five periods."
Matthias ruined Garon's bid for his second shutout this season and 21st overall on his goal with 2:17 to go in the game.
"I don't really care about the shutout," Garon said. "As long as we win, that's most important."
Pyatt gave Tampa Bay a two-goal lead at 3:49 of the second when he made a nifty move at the blue line to get by Florida defenseman Erik Gudbranson and then beat goalie Jacob Markstrom on a back-hander. The goal stopped Pyatt's personal 21-game goal drought, dating to March 20 against Minnesota.
"Bottom line, we weren't good enough," Panthers center Stephen Weiss said.
After Stamkos scored at 6:02, the Lightning took a 4-0 lead on Malone's rebound goal with 9:25 left in the period.
"We're just utilizing our speed, and we have confidence right now," Stamkos said. "When you get confidence, good things happen."
Stamkos has 12 goals and 10 assists in 22 games against Florida.
St. Louis put the Lightning up 1-0 from in close 2:07 into the first. It was his 300th goal with Tampa Bay. St. Louis has 304 goals overall, including four with Calgary from 1998-2000.
"I'm proud of it," St. Louis said. "I'm proud to say that I've been on the same team for 11 years. If you told me 11 years ago I'd score 300 goals, I would have paid money for that."
St. Louis added with a smile that he would have taken simply playing 300 shifts when he first joined the Lightning.
"Quite an impressive individual," Lightning coach Guy Boucher said.
Florida RW Tomas Kopecky, who missed Friday night's game because of back spasms, was back in the lineup. ... Tampa Bay RW Steve Downie sat out his second straight game due to an undisclosed upper body injury. ... Toronto director of player personnel Rick Dudley, who was the Lightning GM when St. Louis was signed as free agent by Tampa Bay July 31, 2000, was at the game.