Radek Dvorak and Olli Jokinen also scored for the Panthers, who won for only the second time in seven road games.
Jochen Hecht and Thomas Vanek scored for Buffalo, which has lost five of its last seven including an overtime loss to Boston on Thursday.
Vokoun, making his sixth straight start, made several solid stops in the first period before the Panthers were able to erupt for three second-period goals on 17 shots.
Sabres goalie Jocelyn Thibault was making just his second start of the season and first in nearly three weeks. He had 20 saves.
Dvorak opened the scoring with his first of the year at 5:32 of the first period, backhanding a rebound past Thibault.
Hecht tied it at 1 with his fourth goal nine minutes into the second period when he also backhanded a rebound in.
The Panthers then broke the game open by scoring three straight goals in a 5:02 span, starting with Zednik's tally with 6:25 left in the middle frame. Standing a couple of feet from the top of the crease, Zednik tapped-in Jozef Stumpel's cross-ice pass for a 2-1 Florida lead.
Zednik made it 3-1 with his fifth of the season three minutes later, putting home his own rebound after Sabres defenseman Andrej Sekera blocked his initial shot.
Jokinen scored his sixth goal in the last five games, and eighth overall, with 1:23 remaining in the second, converting a nifty tic-tac-toe passing play that also involved Nathan Horton and Ville Peltonen.
It was the second straight game in which Florida scored three or more goals in a period. The Panthers scored four third-period goals in their win over Carolina on Wednesday.
Vanek cut the deficit to 4-2 with a power-play goal with 3:23 left in regulation.