Bergenheim put the Panthers ahead for good when he redirected Colby Robak's drive from the left circle into the net. Scottie Upshall and Brandon Pirri also scored for Florida, and. Roberto Luongo made 35 saves and beat Dallas for the first time in five starts.
The Stars still hold a one-point lead over the Phoenix Coyotes for the second Western Conference wild card spot.
Florida erased a 2-0 deficit on goals by Upshall and Pirri in the second period.
The Panthers made it 2-1 when Erik Gudbranson's shot was tipped by a Dallas player, hit Upshall and bounced into the net at 8:20 of the second.
Florida tied when Pirri scored with 57 seconds left in the period. Jimmy Hayes slid a pass to Pirri in the slot for a one-timed shot high into net.
Dallas took the lead 45 seconds into the game when Benn poked the puck past a defender and then wristed a shot past Luongo for his 33rd goal.
Benn, who scored 40 seconds into Saturday night's 5-2 win at Tampa Bay, has three goals in two games.
Dallas made it 2-0 just 39 seconds into the middle period when Seguin scored his 36th of the season during a power play.
A shot from the left circle by Seguin went off the stick of a Florida defender and into the net, giving Seguin his fourth goal in four games.
NOTES: Pirri has a four-game point streak and has 12 points in 15 games. ... Benn has 21 points in 19 games. ... Dallas G Tim Thomas, traded by Florida to the Stars on March 5, didn't play. Thomas been in just two of the past 10 games. ... Dallas forward Ray Whitney missed his second consecutive game because of a lower-body injury.