Belfour made 25 saves to run his career record against Boston to 19-7-3. He has two wins against the Bruins this season.
"We wanted to make a point and show we can compete at a high level and be the type of team that can make the playoffs," Gratton said. "Unfortunately we have those tough starts, like in November, and it hurts us."
Florida has beaten Boston six straight times, including all four meetings this season by a combined 24-10 score. The Panthers also snapped the Bruins' four-game winning streak.
"For some reason, Florida really has our number," said Bruins goalie Tim Thomas, who was pulled after allowing three first-period goals. "We were hoping to change that coming into this game, but I have to guess they played their best games of the year against us."
Boston's Hannu Toivonen replaced Thomas before the second period. Thomas, who won at Tampa Bay on Friday night, allowed three first-period goals on 19 shots. Toivonen stopped 28 shots.
Goals by Peltonen, Weiss and Horton gave Florida a 3-0 first-period lead. Weiss scored on the power play, and Horton scored short-handed.
Horton scored at 19:11 of the first period, when he one-timed a pass from Weiss in the left circle. Horton has seven goals in his past nine games to run his season total to 22.
Weiss scored from in close during a two-man advantage to give the Panthers a 2-0 lead. Jokinen's shot rebounded in front to Gelinas, who passed the puck to Weiss.
"I think we're starting to click and it's showing on the ice," Weiss said. "There's just a lot of positives in a game like this. It's just frustrating that we can't put anything together consistently but when we have a game like this it feels good."
Boston made the most of a 5-on-3 power play midway through the second period, scoring twice within 48 seconds. Savard scored his 21st at 14:09 and Brad Boyes netted his 12th at 14:57 to pull the Bruins to 5-2.
"Florida came after us and generated an attack; we didn't defend well enough and we didn't generate much offense," Bruins coach Dave Lewis said. "Only when we had the power play did we have some quality, quality chances."
Lewis said center Phil Kessel injured his lower body and would be re-evaluated after the team returned to Boston.
Weiss and Gratton also had three points. Jokinen's goal was his team-high 25th. ... Florida hasn't lost to Boston since Nov. 3, 2005. ... The Panthers improved to 10-2-3 in their past 15 home games. ... Boston was seeking its first five-game winning steak since a six-game run from Jan. 29-Feb. 10, 2004. ... Bruins left wing Marco Sturm agreed to a multiyear contract extension earlier Saturday. Terms of the deal were not disclosed. "Maybe in the open market I could have gotten more money, who knows?" Sturm said. "But I'm happy here." ... The Bruins claimed goalie Joey MacDonald off waivers from Detroit, and placed right wing Glen Murray (lower body) on injured reserve.