Versteeg put the Panthers up 5-3 with his second power-play goal of the game, beating goalie Dwayne Roloson from the low right circle 25 seconds into the third period. Florida scored five goals in nine chances with the man advantage.
"We're slowly picking away, and tonight it explodes," Florida coach Kevin Dineen said. "We'd love to take credit for all our schemes, but there was a lot of high-end talent out there. They weren't the pretty plays. They were making real quality plays, and we were getting the puck at the net. That was the difference."
The Panthers went ahead 6-4 when Weiss scored at 15:28 of the third. Jason Garrison added a late power-play goal.
"We moved it around really well, good puck movement," Weiss said. "We were crisp and we shot the puck when we had opportunities, and they went in."
All four of Campbell's assists came on the power play.
"It's just one of those nights, I guess. Things are going good," Campbell said. "That's not going to happen too often, so you'll take it when you get it."
Teddy Purcell, Victor Hedman, Vincent Lecavalier and Steven Stamkos scored for Tampa Bay, which played at home for the first time since its arena underwent around $40 million in offseason improvements. The Lightning had lost four in a row to finish a season-opening, five-game trip 1-2-2.
"Obviously, we're not happy," Stamkos said. "I wouldn't say we're in a panic mode, but we're worried. This isn't the start we wanted. We're taking way too many penalties."
Tampa Bay dropped a seven-game series last season to Boston in the Eastern Conference finals.
Stamkos scored in-close on goalie Jose Theodore to get Tampa Bay within 5-4 at 10:53 of the third.
"This one is done," Tampa Bay coach Guy Boucher said. "Reality is we have to get better."
Goals by Versteeg, on the power play, and Bergenheim during a short-handed breakaway gave Florida a 4-2 lead in the second. Lecavalier cut the Lightning's deficit to 4-3 with 3:39 remaining in the period.
After Kopecky and Purcell traded power-play goals, Hedman gave Tampa Bay a 2-1 lead at the 14:00 mark of the first. Weiss tied it on another man-advantage goal with 2:48 remaining before intermission.
Hedman snapped his 27-game goal drought, which dated to Feb. 17 against Detroit.
Lightning defenseman Marc-Andre Bergeron had three assists. He has six assists and eight points overall this season.
A pregame moment of silence was held for two-time Indianapolis 500 winner Dan Wheldon, who died Sunday after being involved in a fiery 15-car crash at Las Vegas Motor Speedway. Wheldon lived in nearby St. Petersburg. ... Arena improvements in Tampa included new seats and the installation of a pipe organ. ... Florida killed its first nine short-handed situations this season before Purcell scored in the first.