Romell Quioto had given Thierry Henry's Montreal an early lead at Red Bull Arena on Sunday, but his first-half red card proved costly.
Alejandro Bedoya levelled before Kacper Przybylko's brace either side of half-time, and Anthony Fontana sealed the win.
Quioto found the bottom corner with a 25-yard free-kick in just the fifth minute, but he was sent off 11 minutes later for elbowing Mark McKenzie.
Quioto's goal was the first time Montreal had scored from a direct free-kick shot since 2018, according to Opta.
Philadelphia quickly took advantage of the sending off as Bedoya drove home a powerful finish from inside the area to make it 1-1 midway through the first half.
Przybylko headed in Matt Real's cross on the stroke of half-time and the forward put away a Brenden Aaronson pass early in the second half.
Fontana's low 20-yard effort in the 65th minute sealed the win as Philadelphia returned to second, three points behind Columbus Crew, while Montreal are sixth.
Philadelphia has scored eight goals from outside the box this season, which is three more than any other MLS team.