Grabovski's backhander 7:52 into the final period gave the Maple Leafs a 3-1 lead, which they needed after Philadelphia's Jakub Voracek scored on a power play 4 minutes later.
The Flyers applied tremendous pressure in the closing minutes in a bid to score the equalizer, but Ben Scrivens notched 10 third-period saves to secure Toronto's second win in three contests.
Jay McClement sealed the victory with an empty-netter. Nikolai Kulemin also supplied a goal and an assist for the Leafs.
Scrivens finished with 25 saves overall.