Marseille suffered their first defeat under Jorge Sampaoli with a 3-0 loss at Nice on Saturday, while Bruno Genesio's Rennes made it back-to-back wins by beating Metz.
OM had climbed into the European places after two straight victories, but slipped to sixth, below Lens on goal difference, after a poor performance at the Allianz Riviera.
Rennes are only a point behind in the race for the Europa Conference League spot after winning 3-1 at fellow European hopefuls Metz.
Teenager Khephren Thuram scored the opening goal on 34 minutes for Nice, before Amine Gouiri doubled the advantage with 16 minutes to play.
Dario Benedetto had a late strike for Marseille disallowed by VAR for offside, and their misery was compounded when Alexis Claude-Maurice added extra gloss to the scoreline for their Mediterranean-coast rivals in injury time.
"The second goal changed the game. The first half was our best since we arrived," said Sampaoli.
"Unfortunately, we didn't manage to score... As soon as we conceded a goal, the team gave up. We gave up our playing philosophy. We played without control. We played for Nice."
Former Argentina and Chile boss Sampaoli, who took over from Andre Villas-Boas, had led his team to wins over Rennes and Brest.
Rennes backed up their first victory under ex-Lyon coach Genesio, against Strasbourg last weekend, with another impressive display.
Away forward Jeremy Doku netted in the 18th minute before Martin Terrier's penalty seven minutes before half-time.
The 18-year-old Doku was sent off early in the second half, but Serhou Guirassy wrapped up the points for Rennes late on. Papa Ndiaga Yade hit a 90th-minute consolation goal for Metz.
"Perhaps the success that had eluded this team for some time has returned," said Genesio.
"Before talking about Europe, I think we should stay focused on our game. We think about it, we have ambition, but we have to stay focused on our game."
Before the last two wins, Rennes, who played in this season's Champions League group stage, had suffered six consecutive league defeats in a run which cost Julien Stephan his job as coach.