The defeat left them in third place on 77 points, six points behind Paris St Germain, who have a far superior goal difference with two games remaining.
Marseille, who are fifth on 58 points, scored through Bafetimbi Gomis and Patrice Evra either side of a goal from Nice's Italian striker Mario Balotelli.
Leaders Monaco, who have three games left, have 86 points after they beat Nancy 3-0 away on Saturday.
PSG crushed Bastia 5-0 at Parc des Princes on Saturday but Monaco have a much better goal difference and will be virtually certain of being crowned champions if they beat Lille at Louis II next weekend.
Nice were already guaranteed a top-three finish, which brings a place in the Champions League qualifying round.
Marseilles's Gomis opened the scoring at the Velodrome with a near-post header from Dimitri Payet's corner in the 21st minute.
Balotelli equalised five minutes into the second half with a close-range effort only for Evra to restore OM's lead in the 66th with a diving header at the far post.
Earlier, fourth-placed Olympique Lyonnais came from a goal down to beat mid-table Nantes 3-2.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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