John Hayden scored, and Craig Anderson made 25 saves for the Sabres (18-32-8), who have lost eight of their past 10 games.
"The first period was, I don't know what their shot count was (three), but it wasn't high," Buffalo coach Don Granato said. "And when we gave up a little -- the second we gave up too much time and space -- we responded with hesitation, a little bit of fear maybe, and that caused hesitation, the fear not to make a mistake.
"You give skill players and a team like that that little bit extra, too much respect, they can make you look foolish at times. I felt that was a big part of it, big part of it. We just took a step back and we were a little too conservative. They can take advantage of that in a heartbeat."
Montour gave the Panthers a 1-0 lead at 5:22 of the first period when Barkov found him pinching at the bottom of the right circle.
"It was nice," said Montour, who was playing in Buffalo for the first time since being traded on April 10, 2021. "Obviously, it's good to see some good faces. It's obviously a little different playing against them, but it's hockey. Once you get to game time, it's all the same. So obviously, it was good to get that one early and keep going from there."
Noel Acciari made it 2-0 at 5:54 of the second period when he drove down the left wing, held off Sabres defenseman Rasmus Dahlin and shot to the far top corner for his first goal of the season.