Myers' slap shot from well above the right circle went over Tomas Vokoun's left shoulder and into the net for his seventh goal of the season.
Mike Weber and Thomas Vanek also scored for the Sabres, who lost their two previous games against the Panthers this season. Ryan Miller made 24 saves.
Steve Bernier and Marty Reasoner scored for Florida, which has lost five straight home games. Vokoun stopped 24 shots.
Vanek scored at 8:59 of the third, giving Buffalo a 2-1 lead with his seventh goal in his last 11 games. Jason Pominville passed the puck from behind the goal line to the front of the net, where Vanek poked it past Vokoun.
The lead didn't last long. Reasoner took a pass from Dennis Wideman and his wrist shot beat Miller on the stick side, tying it at 2 midway through the period.
The Panthers tied it a 1-all on Bernier's power-play goal in the second. Jason Garrison took a shot from the point and the puck went through traffic and was deflected by Bernier into the back of the net at 18:38.
The Sabres took a 1-0 lead on Weber's goal at 10:22 of the second. The Sabres won the faceoff at the right circle and the puck was sent back to the blue line. Weber took the shot from the point and the puck got through a maze of traffic, glanced off a defensman's skate and past Vokoun.
NOTES: Florida RW Jack Skille, acquired from the Chicago Blackhawks on Wednesday, saw his first action with the Panthers. ... Miller started his 30th consecutive game, dating to Nov. 26th vs. Toronto. Miller's consecutive starts streak is the longest in the NHL this season. ... Vanek has seven goals and seven assists in the last 11 games. The Sabres are 8-2-1 in that span.