Joel Farabee and James van Riemsdyk also scored for the Flyers (25-32-11), who had lost four in a row. Carter Hart made 34 saves.
Tippett gave Philadelphia a 1-0 lead at 15:10 of the first period with a power-play goal.
He scored his second goal at 13:14 of the second period on a one-timer from the left face-off circle to make it 3-0. It was his 20th goal of the season.
Tippett completed the hat trick at 5:33 of the third period to make it 5-1. He was first on a long flip pass out of the defensive zone from Tony DeAngelo, raced in alone on Anderson, deked him to the ice and finished the breakaway.
"He's playing great and just keeps getting better and better," said DeAngelo, who assisted on two of Tippett's three goals. "His speed, you can't defend his speed. He gets a step on you, and he's gone. Too big, too strong, great shot, good finisher. It's good to see somebody taking a step like that and just keep running with it."
Farabee made it 2-0 at 3:53 of the second. He led a 2-on-1 rush with Tyson Foerster, whose shot missed the net, but Farabee recovered the puck off the end boards and slid it under Anderson. It was Farabee's first goal in 27 games, dating back to Jan. 9, when Philadelphia won 4-0 at Buffalo.
"The air came out of the balloon, and we started to press," Sabres captain Kyle Okposo said. "Just a tough second [period] tonight."