"We didn't respond well to pressure," Florida coach Kevin Dineen said. "When they pressured our players, instead of responding to that, understanding that it was coming, I think it created turmoil for us."
Filppula scored consecutive third-period goals to give the Lightning a 6-2 lead.
St. Louis, playing at home for the first time since being selected team captain earlier this month, made it 1-0 off a pass through the slot by Stamkos 8:13 into the game.
St. Louis has 917 points, which moved him past Bobby Orr (915) into 94th place on the NHL all-time list.
"I don't think it's something that you think about when you start your career," St. Louis said. "A pretty special player that I get to pass."
St. Louis' goal marked the first time this season that Tampa Bay took a lead during regulation. The Lightning's other two victories came in overtime and a shootout after third-period comebacks.
Stamkos put the Lightning up 2-0 when he beat goalie Jacob Markstrom for a short-handed goal at 13:54 of the first. It was Tampa Bay's first short-handed goal since Ryan Malone scored one on March 26, 2012.
"You know they're dynamic," Dineen said of Stamkos and St. Louis. "You know that if one guy has the puck, he's looking for the other guy, that they're really highly skilled players, but more than anything, they work as hard as anybody in the league. If you don't match that, if you don't have 100 percent buy-in and effort to try to contain them, you're going to get lit up like we did tonight."
Boyes got the Panthers within 2-1 on a power-play goal 59 seconds into the second. Florida had failed to convert on its previous 17 man-advantage opportunities this season.
Tampa Bay went up 3-1 when Stamkos scored from the right circle with 8:21 left in the second. Ondrej Palat added a late second-period goal.
Huberdeau, last season's Calder Trophy winner as rookie of the year, scored his first goal in nine games early in the third.
Florida G Tim Thomas (groin) said he felt "better" after skating and taking some shots Thursday. Dineen said it's very doubtful that Thomas, who was hurt Tuesday at Philadelphia, will be ready for Friday's home opener. ... Panthers C Shawn Matthias played after missing the morning skate due to flulike symptoms. ... Markstrom was pulled midway through the third after allowing six goals on 24 shots.
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TAMPA, FL - OCTOBER 10: Martin St. Louis #26 of the Tampa Bay Lightning signs autograph while walking the blue...