Gameiro, who had only played 74 minutes this season before on Saturday, opened the scoring in the 10th minute with the first real opportunity of the match.
The France international increased his chances of a regular starting berth by doubling his tally 12 minutes before the interval and although the hosts had several chances in the second half, they could not increase their margin of victory.
PSG started the season with three consecutive draws but had subsequently enjoyed a quick upturn in form with wins over Lille, Toulouse and Bastia, as well as Dynamo Kiev in the Champions League.
And they made an excellent start as they sought to extend that winning run with Javier Pastore releasing Gameiro, who slotted past Sochaux goalkeeper Simon Pouplin after just 10 minutes.
Carlo Ancelotti's men were then forced onto the back foot, however, and Cedric Bakambu was denied on two occasions by fine saves from PSG stopper Salvatore Sirigu.
Sochaux were made to pay for their profligacy when Gameiro doubled his and PSG's tally.
Zlatan Ibrahimovic freed Maxwell down the left and the Brazilian defender's cross picked out Gameiro, who fired across Pouplin and into the net.
But Sirigu once again came to PSG's rescue to produce an outstanding save from Roy Contout's effort from outside the area on the stroke of half-time.
It was all Ancelotti's men in the second half, with Ibrahimovic's overhead kick narrowly missing the target just before the hour mark.
Gameiro then twice missed the opportunity to claim his hat-trick. The 25-year-old's scissor-kick from Ibrahimovic's lay-off was inches wide and the Frenchman's near-post volley produced an excellent save from Pouplin.
Those misses did not come back to haunt PSG, who temporarily moved up to second in Ligue 1.
Information from The Associated Press was used in this report.