It was the first win in six games for Toronto and came against a team that hadn't been beaten in regulation in three weeks.
Lee Stempniak and Pavel Kubina also scored for Toronto. Mike Richards had both Philadelphia goals. The Flyers' six-game winning streak was snapped Friday in a 3-2 overtime loss to Carolina.
Burke was introduced Saturday for the first time since he was hired this week and spoke to the players before the game.
Andre Deveaux and Jamal Mayers both engaged in fights during the first period, something Burke must have enjoyed from his seat in the press box.
"Our team plays a North American game, we're throwbacks," he said before the game. "We don't apologize for that. It's black and blue hockey."
The Leafs scored first when Stempniak netted his first goal since being acquired. He charged to the net, and Moore's hit his left skate and went in at 14:45 of the first period.
Richards tied it 35 seconds later but the Leafs went back ahead during the second period. Antropov had goalie Martin Biron's clearing attempt go off his face before he quickly backhanded the puck in at 2:55.
Moore extended the lead to 3-1 when he stepped out of the penalty box and took a breakaway pass, crashing into the net after beating Biron with a deke at 8:43.
Richards narrowed it to 3-2 by scoring Philadelphia's NHL-leading ninth short-handed goal of the season. He one-timed a pass from Simon Gagne behind goalie Vesa Toskala at 17:23.
A week ago the Maple Leafs squandered a lead in the third period by playing tentatively against Chicago, but they kept coming this time. Kubina wired a screened shot past Biron at 2:16, and Toskala stood tall during a couple of Flyers power plays. He got his glove on a prime scoring chance in close by Gagne.
Toskala finished with 28 saves in his second straight strong outing.
"Rebuilding won't be easy," Burke said. "When you change the general manager, you don't change the team. It will take some time and some effort.
"Changing the general manager doesn't change the roster." Notes: Referee Dan Marouelli worked his 1,500th career game. ... Deveaux appeared in his second career NHL game for the Leafs. He's the first player born in the Bahamas to play in the league. ... Gagne has points in 19 of 22 games. ... Burke was a member of the Flyers organization during his playing days and won the Calder Cup in 1978 with Philadelphia's farm team in Maine.