Vanek and Cody Hodgson had a goal and two assists each, and Alexander Sulzer also scored for Buffalo. For Vanek, he continued his prolific start to the season in taking over the NHL lead with 19 points (eight goals, 11 assists).
The trouble is the Sabres aren't getting production from anyone else, which cost them against the Panthers.
Shortly after Sulzer scored to make it 3-1, second-line center Tyler Ennis was stopped by Jose Theodore on a breakaway. Then third-line center Mikhail Grigorenko and second-line winger Marcus Foligno both missed the net after being set up in the slot.
The Panthers responded with Parros and Mueller scoring to tie the game before the second period was over.
Buffalo, playing its third game in four days, ran out of steam in being outscored 3-0 and outshot 18-5 over the final 30 minutes. The Sabres were outshot 33-20 overall, and 13-4 in the third period when the team didn't get its first shot on net until Jochen Hecht slapped a shot on from the right boards with 8:11 remaining.
Vanek refused to use the team's lack of rest as an excuse.
"No, I don't think so," he said. "Going into the third, no one wanted to make the mistake, and we kind of didn't do much offensively."
The Panthers are finally starting to find their offense, having combined for 10 goals in two games after managing just five in their previous five.
It helps that the Panthers are suddenly getting healthier.
Two games after forward Kris Versteeg returned to the lineup, the Panthers got first-line center Stephen Weiss back on Sunday. Weiss, who missed four games with a lower-body injury, had an assist in setting up Parros' goal.
"We're building character," Weiss said. "We've strung a couple of wins together, which was nice. But as a team, we're now 3-5."