Tampa Bay (46-21-7) won its fourth consecutive game and is one point behind the Montreal Canadiens for first place in the Atlantic Division. The Canadiens lost in overtime 3-2 to the Nashville Predators.
The 46 wins match the most in Lightning history, also accomplished in 2003-04, 2010-11 and last season.
Florida (33-26-14) is five points behind the Ottawa Senators for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"It is disappointing," Panthers center Jonathan Huberdeau said. "We want to make the playoffs. We needed these two points. We needed it and it didn't happen. We can't do anything about it now, but just focus on our game and we have to come out stronger against [the Toronto Maple Leafs on Thursday]."
Callahan took a pass from behind the net and skated around to the front to beat Florida goalie Roberto Luongo with a wrist shot from close range for his 22nd goal of the season.
"I thought we responded well in the third period and showed some patience after we tied the game," Callahan said. "When we play the right way, we are a tough team to play against. We have to realize that and do it for a full 60 [minutes]."
"I think we got those two quick ones early, much like the Boston game (a 5-3 win Sunday) and maybe we thought it was going to be a little easier than it was," Lightning coach Jon Cooper said. "I'll tell you of all the teams, and we've played them all, that's one of the hardest teams we play against, by far."
Jussi Jokinen made it 2-1 at 6:16 with a wrist shot from the right circle that beat Lightning goalie Andrei Vasilevskiy high on the glove side. Brandon Pirri tied the game 16 seconds later with a wrist shot from the point after Vasilevskiy lost his stick and was in the process of retrieving it from Tyler Johnson.
"We battled back and we took the lead but that last goal killed us," Panthers coach Gerard Gallant said. "We played well, it's a disappointing loss. We gave up three weak goals, not by the goaltending but by defensive-zone coverage and not battling, not working. We played hard, but you can't give up three goals like that."
Florida took a 3-2 lead at 8:14 when Huberdeau scored on a rebound of his shot.
"I think we got away from our game a little bit, but credit to Florida because they played a lot harder and were more desperate than us when they got those three goals," Johnson said. "We had a mental lapse in the second period but luckily it was just for 20 minutes. You try to look at the positive and say the team battled back in the third."
Tampa Bay tied it 3-3 at 1:30 of the third period on Nikita Kucherov's 27th goal of the season. Kucherov took control of a loose puck behind the net after Andrej Sustr's slap shot went above the goal and scored on a wraparound against Luongo.
"It was really tough," Luongo said. "They are a team that is good around the net. Bottom line, I've just got to be better … you want to make a save when it's important. This is a tough one to digest."