Lyon had earlier beaten Nantes 1-0 at Stade Gerland to go top, meaning Monaco needed a win to move back to the summit.
Monaco went ahead at the Stade Louis II when Fernando Morientes hammered home a penalty on the hour.
Just when it looked like Didier Deschamps's side was going back top, Sochaux struck as Mathieu swung in a free kick which deceived everybody and flew into the corner.
Lyon went to the top of Le Championnat after their 1-0 home success over Nantes.
Giovane Elber grabbed the only goal of the game after 25 minutes.
The former Bayern Munich hit-man did really well to finish past Mickael Landreau as he slipped just before slotting home.
Lyon held on to claim all three points, but had to cope with just ten men for the remaining nine minutes, as Florent Malouda was dismissed for his second bookable offence.
Paris Saint Germain stayed third and closed the gap on Monaco to just three points after their 1-0 win over Ajaccio at Parc des Princes.
Portuguese striker Pedro Pauleta hammered home from the spot after 68 minutes.
Cameroonian Valery Mezague grabbed the only goal of the game as Auxerre went down 1-0 at lowly Montpellier.
Mezague slotted home a penalty just after the interval, although his day took a turn for the worst when he was dismissed on the hour.
However, Montpellier held on but they remain second from bottom as Metz beat Strasbourg 1-0 at Stade Saint Symphorien.
Mehdi Meniri pounced after 18 minutes to give his side the win - a victory which lifts them out of the relegation zone - at the expense of Ajaccio.
Bordeaux's poor season continued as they were held to a 1-1 draw by Nice at Stade Chaban-Delmas.
Lilian Laslandes put Nice ahead after 11 minutes, before David Jemmali levelled just before half time.
Nice had Sammy Traore dismissed in the latter stages, but they held on for a good point.
Lens and Lille remain in ninth and tenth respectively - after they played out a 1-1 draw at Stade Grimonprez-Jooris.
Lens went ahead after just six minutes when Charles-Edouard Coridon scored, but Lille fought their way back as Matt Moussilou fired home on the half hour.
The visitors then had Papa Bouba Diop (second bookable offence) and Rigobert Song (foul and abusive language) sent off in the 55th minute.
Lille, though, could not take advantage of their extra two men and Lens held out for a share of the spoils.
The final game of the evening saw bottom-of-the-table Le Mans grab a goalless draw at Bastia.
Click below for match summaries:
Bastia 0-0 Le Mans
Bordeaux 1-1 Nice
Lille 1-1 Lens
Lyon 1-0 Nantes
Metz 1-0 Strasbourg
Monaco 1-1 Sochaux
Montpellier 1-0 Auxerre
PSG 1-0 Ajaccio
Click here for an updated Ligue 1 table.
