Yannick Ferreira Carrasco had put Claudio Ranieri's side 2-0 up after 10 minutes, but Sochaux, in coach Herve Renard's first game in charge, fought back after the break with goals by Cedric Bakambu and Joseph Lopy.
Monaco have 22 points from 10 games to PSG's 24 after the French champions hammered Bastia 4-0 at home on Saturday.
Sochaux, who had lost six of their nine opening games in Ligue 1, remained second from bottom on six points.
Monaco got off to a great start, with Ferreira latching on to a Marcel Tisserand cross in the fifth minute and doubling the tally five minutes later by firing past Simon Pouplin after intercepting a poor back pass by Carlao.
Monaco were without France defender Eric Abidal, who pulled out following a thigh injury scare during warm up.
"It's nothing serious," Abidal told BeIN Sport. "I had that pain yesterday and we did not want to take any risk. I'd rather lose three days than three weeks."
Sochaux stepped up a gear after the interval and striker Bakambu reduced the arrears with a powerful header 11 minutes into the second half.
Thirteen minutes later, Lopy equalised with a header at the far post from Rafael Dias's corner kick.
In the late kick-off, Lyon needed an injury-time strike to rescue a 1-1 draw at home against Bordeaux but remain in the bottom half of the table.
Ludovic Obraniak had Bordeaux in front after 62 minutes but Lyon - who lost Alexandre Lacazette to a red card - had to wait until the first minute of added time for Jimmy Briand to find an equaliser.
Elsewhere, St Etienne went seventh with a 3-2 win over Lorient.