Striker Bafetimbi Gomis looked to be offside when he grabbed the 17th minute opener after a good cross by Brazil's Michel Bastos, who then netted himself with a diagonal effort on the half hour.
The result sent rookie coach Remi Garde's side, champions seven times in a row from 2002-2008 before a barren spell, top with 14 points from six games and left fellow big guns Marseille with just three points.
Marseille were champions in 2010 and second to Lille last term but Deschamps' position could now come under scrutiny after a dull display albeit without injured forward Andre-Pierre Gignac and against a strong side.
Paris Saint-Germain earlier fought back from two down to draw 2-2 at promoted Evian.
Big-spending PSG had won six games in a row in all competitions but their rich Qatari backers will not have been impressed with dropped points at a promoted team despite the determined comeback.
Jerome Leroy's goal and a Yannick Sagbo penalty gave Evian clear water before a magical strike from record French signing Javier Pastore, his second in two league games, brought PSG back into the game just before the break.
Mathieu Bodmer grabbed the equaliser nine minutes from time following a free-kick into the box.
"We've got to forget this idea that we can beat everyone 5-0," PSG coach Antoine Kombouare told reporters.
"We were playing against a good side who work hard, a coach who has done his homework and motivated players. If you don't respect them, you will end up being second in the tackles."
PSG moved level on 11 points with fourth-placed Lille, Lorient and Stade Rennes, who drew 1-1 at home with lowly Nancy.
Second-placed Montpellier drew 2-2 at Stade Brest on Saturday, Toulouse in third produced a stirring comeback to beat Girondins Bordeaux 3-2 while champions Lille were held 2-2 at home by Sochaux.
