Victor Olofsson scored for the Sabres (16-13-7), and Carter Hutton made 23 saves.
"Nobody played a good game tonight and that's frustrating," Sabres forward Kyle Okposo said. "Losing Jack right before the game, that's a time for guys to step up and nobody did it."
The Flyers scored three times in 4:01 of the first period. Mikhail Vorobyev made it 1-0 when his pass from the left circle went off the stick of Sabres forward Conor Sheary and past Hutton at 13:04.
Van Riemsdyk made it 2-0 at 15:32. Ralph Krueger used a coach's challenge for goaltender interference but the call on the ice was upheld.
The Sabres were assessed a penalty for delay of game, and on the ensuing power play, Matt Niskanen scored to make it 3-0 at 17:05.
Ivan Provorov's power-play goal gave the Flyers a 4-0 lead at 8:20 of the second period. Pitlick made it 5-0 at 9:22, and van Riemsdyk scored on the power play to make it 6-0 at 12:27.
Van Riemsdyk has 10 points (six goals, four assists) in his past 11 games, after he had nine points (four goals, five assists) in his first 24.
"Obviously now some pucks are going in," van Riemsdyk said. "I'd like to think I was doing a lot of good things the first half of the year. For whatever reason pucks weren't going in, but now want to keep it rolling here."
Flyers coach Alain Vigneault said they will need more from van Riemsdyk without Oskar Lindblom, who likely will not play again this season while being treated for Ewing's sarcoma, a form of bone cancer. Lindblom, whose diagnosis was announced Friday, is tied with Claude Giroux for the Flyers lead in goals with 11.
"We need [van Riemsdyk] to continue," Vigneault said. "I need him to play well with the loss of Oskar on the left side. We need him to step up and play important minutes and do what he is doing for us right now."
Olofsson's power-play goal made 6-1 at 11:35 of the third period.
"It's no consolation that you get one in the third period," Krueger said. "It's what happened on the way to get there. It's disappointing. We got hit hard here tonight."
