Scott Laughton scored with 37 seconds left in the second period from the high slot to extend the lead to 3-1. He has five points (three goals, two assists) during an NHL career-high five-game point streak.
"We said it from the beginning to be ready, and they kind of jumped on us and then we kind of found our feet," Laughton said. "We did a really good job in the second period with sustained pressure in the zone and our [defensemen] were moving pretty well, cycling around the zone. I thought we did a good job in the later part of the game."
Chlapik, who was recalled from Belleville of the American Hockey League earlier Monday and arrived about two hours before puck drop, scored his first goal of the season to cut it to 3-2 at 17:03 of the third period. He replaced Colin White, who was out with an upper-body injury.
The Flyers played without forward Jakub Voracek, who is third on Philadelphia with 61 points (18 goals, 43 assists) and was serving the first of a two-game suspension for interference against the New York Islanders defenseman Johnny Boychuk on Sunday.