Versteeg also scored a goal for Florida, while Scott Clemmensen stopped 20 shots. Versteeg, the team's leading scorer with 20 goals, returned to the lineup after missing Wednesday's game against the Capitals with the flu. He still suffered from its effects, and said he felt ''pretty much terrible'' before the game.
''It's been a rough little go over the last few days,'' Versteeg said. ''Hopefully over the next little while I start to feel better, but a win always makes you feel pretty good.''
Bryan Little scored for Winnipeg, and Chris Mason made 28 saves.
Winnipeg lost for the ninth straight time when playing the second of consecutive games. The Jets are have been shut out twice and outscored 36-7 in those.
''If you're going to be a good team, you have to learn to win these games,'' Little said. ''We can't use that as an excuse. Every team in the league has to play back-to-back games.''
Winnipeg has scored two goals or fewer in its last five games and nine of the last 11.
''Our team right now can't give up 20 minutes of free play and expect you're going to be able to win the game,'' Jets coach Claude Noel said.
''Do I like the one goal we get every game? No. Would I Iike to see it change? Yes. Do I coach that way? No. That's what we have, but there's still a way to win the games.''
The Jets tied the game 1-1 on Little's goal in the second. Little grabbed a loose puck and took a wrist shot from the left circle. The puck went between Clemmensen's pads at 11:29.
Florida regained the lead about three minutes later. Marcel Goc passed the puck from behind the net to Bergenheim, who was waiting in front of the crease. His wrister got past Mason at 14:27.
The Panthers increased their hold on first place in the Southeast Division, moving three points ahead of the Capitals (56) and five points ahead of Winnipeg (54).
''We know what's at stake every game and we've got to start putting a long winning streak together instead of winning one and losing one,'' Versteeg said.
The Panthers took a 1-0 lead on Versteeg's power-play goal in the first period. Versteeg took a pass from Mikael Samuelsson at the left circle. His slapshot got between Mason's right skate and the post at 15:46. Versteeg now has six goals and two assists in the past three games against Winnipeg.
The last seven games for the Panthers have been decided by two goals or fewer.
''If you look at our record in the last two months, so many tight games, close games, I like the idea that we're building up some resiliency and some character,'' Panthers coach Kevin Dineen said.
''I think that will pay up for us down the line. We'd like to have a game where we have a little breathing room, but we're getting used to these kinds of games and it's the nature of the league right now.''