With time winding down in the extra session, Giroux flew down the right wing into the zone and from the circle he snapped a laser on net, using Duncan Keith as a screen, and it went in and out of the left corner for the win.
Scott Hartnell scored the other two goals while Ray Emery allowed two early goals in the first period, but finished the game with 23 saves for the Flyers, who have ripped of three straight wins and six of eight.
Andrew Shaw and Keith had the goals for Chicago, which has lost three of its last four games. Antti Raanta gave up all three goals on 37 shots.
It was a quick start for Chicago as Shaw scored just 2:29 in off a blocked shot from Michal Handzus, and it was a 2-0 game at 3:51 when Jonathan Toews sent the disc from the right corner to the slot where Keith's big blast trickled past Emery.
Philly, though, got one back two minutes later thanks to a lucky break as Hartnell was behind the net and tried to send the puck to the left wing, but it hit off Marcus Kruger and snuck past Raanta.
The Flyers tied the game at 16:27 of the first when Giroux centered the puck from the left of the net and Hartnell one-timed it in for his 18th of the year.
A spirited second period saw each team get a power play and a total of 17 shots thrown on net, 11 by Chicago, but neither side was able to put one in and the game headed to the third period still tied.
The Flyers appeared to take the lead with 6:12 to play when Brayden Schenn put in the puck from down low after it hit the post off a Vincent Lecavalier deflection, but the goal was waived off as Lecavalier had hit the puck with a high stick.
Late in regulation Steve Downie backhanded the puck from the left side past a sprawling Raanta. Schenn had a chance to knock it in, but his shot went off the post and the game went to overtime.