Sebastien Corchia had a chance for the home side inside the first minute, but his effort went well over the bar.
Yohan Cabaye had PSG's first real chance on 17 minutes, but the midfielder couldn't make the most of it and missed the target by some distance.
The away side eventually took the lead on 25 minutes through Edinson Cavani, who brought down Thago Motta's expertly and volleyed past the goalkeeper.
Ezequiel Lavezzi had a chance just after the half-hour mark, but he blazed his shot over the bar.
Lucas Moura had an attempt on goal from long distance, but his effort went wide of the mark.
Sochaux started the second half well and began to test PSG's backline when they pushed forward.
The home side equalised on 56 minutes through an own goal by Thago Silva.
Nathan Sinkala came close again for Sochaux, curling a right-footed shot towards the left corner from outside the box; however, it went just wide of the post.
Marco Verratti had an effort saved on 65 minutes as PSG pushed forward in a bid to regain their lead.
Both sides went for the win in the closing stages, with Javier Pastore going close on 85 minutes with a shot from distance that was saved well by the goalkeeper.
A minute later, Sinkala came close again with a strike on the edge of the area after being set up by Jordan Ayew.