Giroud treble sends Montpellier top of Ligue 1
France international Giroud poked home five minutes into the second half and scored twice more in the closing stages after Abdoul Razzagui Camara had equalised for Sochaux.
Champions Lille stayed in the hunt in third place on 28 points after goals either side of the interval by Dimitri Payet and Moussa Sow gave them a 2-0 home win against Stade Brest.
Fourth-placed Stade Rennes, also on 28 points, beat promoted Evian Thonon Gaillard 3-2 with a double by Julien Feret.
Giroud, who won his first two France caps earlier this month in friendlies against the United States and Belgium, followed up on a John Utaka lob in the 50th minute and poked the ball home to open the scoring.
Camara equalised from inside a packed goalmouth in the 84th minute but the visitors did not wilt.
Giroud made it 2-1 with a fine lob in the 87th minute and put the result beyond doubt two minutes later from close range after collecting a clever through ball from Younes Belhanda, taking his season tally to 12 goals.
"We knew that Sochaux were dangerous against the big guns so it could not be an easy game," Giroud told French TV channel Foot Plus.
"We are settling in the higher part of the table. We played our football in the second half and we were rewarded for it despite a late scare.
"It's a very good start to the season but there is still room for improvement."
One week after beating PSG at the Parc des Princes, Nancy lost 2-1 at home to Dijon and were lying third from bottom on 14 points.
Girondins Bordeaux eased away from the relegation zone with a 2-0 home victory against Caen.
Saint-Etienne beat bottom side AC Ajaccio 3-1, their fourth win in their last six league outings, to move up to seventh on 23 points.