OM looked set for a deserved win after Jordan Ayew gave them a 2-1 lead in the 82nd minute, but Rennes equalised when Mandanda mishandled a routine cross from Abdoulaye Sane.
The ball bounced on to the near post and into the path of Romain Alessandrini who poked it home two minutes from time.
The result left Elie Baup's side in third place with 42 points from 22 matches, three behind leaders Lyon.
Second-placed Paris St Germain will reclaim the lead if they avoid defeat against Lille at the Parc des Princes on Sunday (2000 GMT).
Champions Montpellier climbed to seventh on 32 points after first-half goals by Emmanuel Herrera and John Utaka sealed a straightforward 2-0 home win over Sochaux.
At Rennes's Stade de la Route de Lorient, OM started well, with Andre-Pierre Gignac's volley on the turn going just wide in the 10th minute.
Alessandrini went close for the hosts a few minutes later when he his fierce angled shot flew just over the bar.
OM, however, were sharper and a week after the Ayew brothers scored one each in a 3-2 win over Montpellier, they were at it again.
In the 37th minute, Andre launched a swift counter-attack and played a one-two with Mathieu Valbuena who set him up with a delightful through ball for the Ghana striker to beat Benoit Costil with a low crossed shot.
Mandanda pulled off a great save to deny Mevlut Erding from close range early in the second half but there was nothing he could do when the unmarked Kevin Theophile Catherine headed into the top corner in the 58th minute for the Rennes equaliser.
Jordan Ayew gave the visitors the lead with eight minutes left when he latched on to a Morgan Amalfitano cross.
However, Rennes, who are fourth on 36 points, refused to lie down and Sane's run left Jeremy Morel stranded and his cross from the right caused Mandanda's error.
Basement side Nancy and second-bottom Troyes snatched 2-1 home victories over Lorient and Stade Brest respectively.
Nancy have 15 points and Troyes 16, six and five points from safety.