Giroux ended the second round by using multiple stick fakes to pull Jonas Gustavsson out of position before flipping a shot under the crossbar from the left side.
Phil Kessel tried to sneak his shot home inside the right post, but Ilya Bryzgalov flashed his pad to end the game.
It is the continuation of a tremendous stretch for the 31-year-old, who notched his fifth shutout of the season and third in four starts.
Bryzgalov stopped 29 shots through 65 minutes for the Flyers, who have beaten Toronto in all three meetings this year.
Gustavsson ended with 27 saves for the Maple Leafs, who skidded to their ninth loss in 10.
The Philly netminder made six saves in the first period, matched by eight stops for Gustavsson.
Bryzgalov made progressively tougher saves through the second period, none better than point-blank stops on Matt Frattin and Mikhail Grabovski on separate Toronto power plays minutes apart late in the second period.
Nikolai Kulemin appeared to have a slam-dunk in the first 40 seconds of the third, but his uncontested whack at the left side hit the post instead.
Foreshadowing his later, more important save, Bryzgalov stoned Kessel on a clear breakaway just over 30 seconds into OT.
Martin Biron was the last Flyers goaltender to post back-to-back shutouts in the regular season, on April 4-6, 2008 against the Devils and Penguins...Bryzgalov has stopped 128 of the last 130 shots he has faced.