Dan Vladar made 20 saves for Philadelphia (28-22-11), which had its three-game winning streak end.
The Flyers' 16 shots on goal matched a season low.
"We were soft," Flyers coach Rick Tocchet said. "Execution was tough. We had some chances. We had about three or four 4-on-2's, a couple of chances, hopefully one would go in. ... It's one of those games where you have a tough time saying who had a good game."
Vanecek had a role in that, with his first shutout since March 8, 2025, against the Buffalo Sabres.
His best save came with 1:54 left in the first period, when a shot from the point by Flyers defenseman Noah Juulsen was blocked but rolled to forward Bobby Brink just to Vanecek's left. The goalie lunged forward and was able to glove the shot.
"The puck gets on the side, and I just tried to push hard as possible and then put my glove forward, and then he hit it," Vanecek said. "So, really happy for that."
He made another lunging glove save to rob forward Noah Cates on a shot from the left side with 15:19 remaining in the second period.
"He's a [heck] of a pro, great guy, works hard," Mammoth coach Andre Tourigny said. "With the break, I don't know when exactly (was) his last game, but it was a while back. It was a tough situation. ... I think he's been put in tough spots, often on the back end of the back-to-backs, stuff like that. So, I think he gives us a chance to win when he's in there, and that's what's important."
Vanecek admitted the long breaks between games have been tough mentally. It was his 15th game of the season and just the third since the calendar turned to 2026.
"That was really tough, I'm not going to lie," Vanecek said. "Always when you come back, it's hard to breathe. It's not same with practice, the game is always different. But you're trying to just dial in in practice and then do what you do in the games. That's the only thing I can do, and then wait when I get the chance."
Schmaltz scored a power-play goal at 1:38 of the second period to give the Mammoth a 1-0 lead. Guenther drew the attention of all four Flyers penalty killers as he cut through the middle of the zone and then slipped a backhand pass to Schmaltz, who scored on a sharp-angled snap shot from along the goal line.