Stephen Weiss and Olli Jokinen also scored for the Panthers, who won back-to-back games for just the second time this season. Florida hadn't won consecutive games since Oct. 11-13, when it beat Carolina and Tampa Bay.
Daniel Briere scored for Buffalo and Ryan Miller stopped 35 shots.
Jackman's goal put Florida ahead 2-1 less than a minute into the third period. Nathan Horton brought the puck down the ice to the right circle, then backhanded to Jackman, who put the puck past Miller for his first goal of the season.
The Panthers stretched their lead to 3-1 on a power-play goal with 5:53 remaining when Weiss poked in the rebound of a Jay Bouwmeester shot that caromed off Miller's left leg.
Buffalo tied the score at 1 during a 5-on-3 power play in the second. Chris Drury's shot was blocked by Auld but Briere picked up the loose puck and slipped it by Auld into the right corner of the net at 19:27. The Sabres had taken only seven shots on goal to that point but got off six with the two-man advantage.
The Panthers took a 1-0 lead on Jokinen's power-play goal at 4:53 of the second. Weiss took a shot from the left circle that Miller blocked, and Jokinen was there to drill the puck past Miller's outstretched left leg.
Notes: Briere has seven goals and 13 points in 13 games against Florida ... Jokinen has three goals and four assists during a four-game points streak at home ...The Panthers played their first game without 20-year veteran Joe Nieuwendyk, who retired Wednesday due to chronic back ailments.