Giroud, who had not been called up since his country were knocked out in the last 16 of the European Championship last year, cancelled out Nicolas Pepe's opener to move four goals shy of Thierry Henry's France all-time scoring record before Aurelie Tchouameni wrapped up the win in stoppage time.
The former Arsenal striker who rarely disappointed coach Didier Deschamps despite limited playing time when he was at Chelsea, was included in the squad following Karim Benzema's injury.
He started alongside Christopher Nkunku as Kylian Mbappe sat on the bench after suffering from an ear, nose and throat infection earlier this week.
France next take on South Africa in Lille on Tuesday.
They got off to a shaky start but once they found their groove, threatened more than their opponents as Paul Pogba and Tchouameni bossed the midfield at a packed Stade Velodrome.
Pepe burst into the area and fired a low cross-shot from the near post that beat goalkeeper Hugo Lloris after 19 minutes as the French defence was caught napping.
It took France three minutes to react with Giroud heading home from his clubmate Theo Hernandez for the equaliser.
Les Bleus continued to push and Nkunku came close in the opening half but his header went just too high.
They were however rewarded three minutes into added time when Tchouameni headed his first goal from eight appearances off Matteo Guendouzi's corner.