Lille midfielder Benoit Pedretti, signed from Auxerre in the close-season, headed the opener from an Eden Hazard assist shortly before Debuchy was carelessly sent off for a second booking following a late tackle after 55 minutes.
Cedric Bakambu took advantage of Sochaux's extra man to equalise 20 minutes from time before Lille, who also drew 2-2 with CSKA Moscow in the Champions League in midweek, were awarded a fortunate penalty which Hazard converted.
However, Sochaux's Privat levelled the score four minutes from time with an excellent header as Lille, even with Joe Cole making his first start, finally wilted in heavy rain.
Montpellier, who are two points above Lille on 13 from six games, lead Toulouse on goal difference after they let a two-goal lead slip in a 2-2 draw at Stade Brest.
Toulouse produced a fine comeback of their own to join the leaders after coming from two goals down to win 3-2 late on at home to Bordeaux, whose woes continued despite Cheick Diabate's first-half double.
"I dreamt about this during the four months I was injured," Emmanuel Riviere, who grabbed the added-time winner with his first Toulouse goal, told reporters.
SPARKLING START
Montpellier's Olivier Giroud, pushing for a first France call-up after a sparkling start to the campaign, opened the scoring after 19 minutes and doubled the lead four minutes before the break with a diving header.
Eden Ben Basat pulled one back after 69 minutes for hosts Stade Brest and their Argentine defender Santiago Gentiletti completed the comeback following a corner before they had Tripy Makonda sent off after a scuffle.
Lorient joined Lyon and Lille on 11 points after ex-Arsenal forward Jeremie Aliadiere, without a club last term, headed in the first goal and beat the goalkeeper in a one-on-one for his second in a 3-0 win at home to Saint-Etienne.
Nice overcame Ajaccio 3-0 on the Cote D'Azur, Auxerre and Caen drew 1-1 and Valenciennes battered promoted Dijon 4-0.
