Midfielder Abdoulaye Doucoure scored the only goal in the 76th minute to earn Rennes their eighth Ligue 1 win of the season and halt a three-game losing run.
OM have yet to pick up a win this month following defeats to Paris Saint-Germain, Nice and a 1-1 draw against Reims, and lie sixth in the standings.
Toulouse's European aspirations also suffered a setback with a 1-1 draw against Evian.
Wissam Ben Yedder's goal after 56 minutes looked to have earned the home side the points until substitute Clarck Nsikulu's last-minute equaliser for Evian.
Bordeaux effectively ended Nice's slim hopes of securing a Europa League spot after the two sides played out a 1-1 stalemate.
Nice came into the match four points behind their opponents and 10 behind fourth place, knowing that anything but a win would virtually end their chances of catching St Etienne.
And while Alexy Bosetti did cancel out Jussie's second-half penalty, the visitors could not find a winning goal despite the dismissal of Abdou Traore with four minutes remaining.
First-half goals from Florian Raspentino and Gianni Bruno gave Bastia a 2-0 win over Reims which should satisfy any worries they have about relegation, with Frederic Hantz's men now 12 points clear of the drop zone.
Nantes ended a shocking run of form - and pulled eight points clear of the bottom three - by beating Montpellier 2-1 in a dramatic clash which also saw two red cards and a missed penalty.
Goals in the opening 20 minutes from Serge Gapke and Koffi Djidji set the home side on their way to victory, before Djidji then scored at the other end to give Montpellier a route back into the match.
However, red cards for Joris Marveaux and Daniel Congre then effectively ended the visitors' challenge, before Nantes missed the chance to extend their lead when Itay Shechter saw his spot-kick saved.
Teenage substitute Issa Baradji fired a late double to hand Ajaccio a rare 3-2 win and scupper the hopes Valenciennes had of escaping the relegation zone.
With five minutes remaining, Valenciennes were on the point of climbing out of the bottom three, leading 2-1 and just needing to see out the closing stages.
Eighteen-year-old Baradji intervened though in dramatic style, grabbing an 87th-minute equaliser and a late winner to earn the visitors their success.
Majeed Waris scored in the 51st and 72nd minutes for Valenciennes, with Benjamin Andre netting between those goals for the away side and Baradji breaking home hearts.