Jason Woolley and Chris Gratton also scored for the Sabres, who are on a 3-0-1 roll.
With four games left in their season, the Sabres jumped into 10th place -- a point ahead of the New York Rangers -- and crept within four points of the eighth-place Montreal Canadiens in the Eastern Conference.
Sabres goaltender Martin Biron, who stopped 20 shots, had his shutout bid snapped when Kristian Huselius scored a power-play goal with 1 minute 27 seconds left. The goal came on a two-man advantage after Panthers Coach Mike Keenan pulled goalie Trevor Kidd a minute earlier.
Otherwise, Florida, eliminated from playoff contention long ago, looked flat in kicking off a four-game road trip.
Pyatt opened the scoring 5:42 into the second period. Jay McKee set up the goal when he kept the puck in at the left point and fired a hard pass into the slot, where Pyatt redirected it in over a sliding Kidd.
"That's part of being a team, when some of the top guys are out of the lineup other guys have to step up," said Pyatt, recording the second multipoint game of his career. "You feel like you're a little more part of it, when someone goes down, to play a little more and get a chance to contribute."
Woolley's goal came 12 minutes later. Curtis Brown chased down a loose puck behind the Florida net and centered to Woolley, who scored from the slot.