Matthew Tkachuk finished with three assists for Florida and extended his point streak to seven games. Brandon Montour, Sam Bennett and Anton Lundell also scored for the Panthers.
Florida (46 points) moved two points ahead of Buffalo (44) and into fourth place in the Atlantic Division with the win in the opener of a three-game road trip against Atlantic Division opponents.
''I thought we played a pretty solid road game,'' Tkachuk said.
After splitting a four-game road trip out West earlier in the month, the Panthers improved to 10-14-1 on the road. They have won five of seven overall for the first time this season.
''We haven't had the best road record this year,'' Tkachuk said. ''You can come up with every excuse in the book, but we let a few go earlier this year, and this is a big-time game for us.''
Sergei Bobrovsky made 28 saves for his fourth win in five starts.
''We need that kind of goaltending,'' Panthers coach Paul Maurice said. ''He's battling in the net. He's a little bit acrobatic, but he's intense. And the guys like it. It looks good from the bench. He's making big saves. Everybody is kind of rallying around him.''
Alex Tuch scored for the Sabres, who have lost four of their last five games. Ukko-Pekka Luukkonen stopped 30 shots.
''We got to be better in front of him,'' Tuch said. ''He deserved a win today and we weren't able to help him out.''
Tkachuk fed Verhaeghe for his 20th goal of the season with 1:38 remaining in the third period.
Former Sabre Sam Reinhart set up Lundell on a 2-on-1 to give the Panthers a three-goal lead 34 seconds into the third period.
Bennett scored his 10th goal of the season to make it 2-0 at 8:04 into the second period. Verhaeghe's backhand pass to Tkachuk bounced back to a wide-open Bennett in the right circle.
Montour put the Panthers ahead four minutes in the first period when he crashed the net and knocked in a rebound. The former Sabres defenseman has eight goals this season.
''It was solid from the start,'' Tkachuk said. ''I think the first 10 minutes were awesome.''
Tuch's 21st goal of the season with 8:33 remaining in the third period spoiled Bobrovsky's bid for a second shutout this season.
''We just didn't quite start on time today,'' Sabres captain Kyle Okposo said. ''They obviously had some jump. It's a big game, they knew it right away, and they jumped on us. When we realized we were in a fight, it was a little too late.''
Panthers: Called up forward Grigori Denisenko after placing Zac Dalpe on waivers Saturday.
Sabres: Loaned forward Peyton Krebs to the minors in a paper transaction to create roster spot for Luukonen's recall.
Panthers: At Toronto on Tuesday night.
Sabres: At Chicago on Tuesday night.
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