The Flyers - outplayed over the last two periods and outshot, 40-27, for the game - killed three late penalties to hold off a furious Vancouver comeback.
With a sellout crowd watching their home opener at the Wells Fargo Center, the Flyers blew 3-1 and 4-2 leads before Meszaros took a pass from Kimmo Timonen, skated into the left circle, and beat Roberto Luongo with a high shot to the glove side. That put the Flyers ahead, 5-4, with 15 minutes, 20 seconds left.
Sixty-one seconds earlier, Daniel Sedin's power-play goal had knotted the score at 4.
Giroux (goal, two assists) already has three goals.
"I feel so lucky to play with two people like that," Giroux said of linemates James van Riemsdyk and Jaromir Jagr. "They win all the battles, and they're doing a good job of finding me in the slot."
Giroux has scored a goal in each of the Flyers' three games - wins over defending Stanley Cup champion Boston, New Jersey, and Cup finalist Vancouver.
On Saturday, when Mike Richards and the Los Angeles Kings visit the Wells Fargo Center, the Flyers will try to go to 4-0 for the eighth time in their history - and first since 1995.
Giroux had three points in the opening period as the Flyers - aided by two power-play goals in four early chances - built a 3-1 lead against a Vancouver team that took Boston to Game 7 in last June's Stanley Cup Finals.
But Henrik Sedin, who injured his hip in the previous game, took advantage of a Flyers turnover and scored on a rebound, trimming the deficit to 3-2 early in the second period.
For the second time in the game, however, the Flyers answered quickly. Winger Jakub Voracek scored from the left circle after a nice set up by Sean Couturier, who notched his first NHL point. The goal was scored 1:51 after Sedin's.
"It was a great pass," said Voracek, who has two goals in three games. "I just tried to put it up high."
In effect, Couturier and Voracek were acquired in the deal that sent Jeff Carter to Columbus in June. Couturier, 18, who is making a strong bid to remain with the Flyers for the entire season, was selected by the Flyers with the eighth overall pick in the draft.
With about six minutes left in the second period, Couturier's bid for his first NHL goal clanked off the right post.
About 11/2 minutes later, Vancouver inched to within 4-3 as Chris Higgins snuck behind the Flyers defense and scored from the side of the net.
Jagr had a great chance to increase the lead with 19.6 seconds left in the second period, but he was unable to lift the puck over a prone Luongo, who was able to control the puck while down on the ice.
Earlier, power-play goals by Giroux and Chris Pronger had given the Flyers a 2-0 lead. Giroux scored after Pronger's long pass took a crazy carom off the boards and onto the little center's stick in front of the net. Pronger, off a feed from Giroux, scored on a point drive, with Wayne Simmonds screening Luongo.
The Canucks cut it to 2-1 on a Mikael Samuelsson goal, but just 1:13 later, van Riemsdyk converted his own rebound to put the Flyers ahead, 3-1, with 2:12 left in the first.
Contact staff writer Sam Carchidi at email@example.com or @BroadStBull on Twitter.