Marseille were heading for victory after Jordan Ayew volleyed home with seven minutes to go, however Rennes were not finished and Alessandrini tapped home a simple goal two minutes from the end after goalkeeper Steve Mandanda parried the ball into his path.
Earlier in the game, Andre Ayew put Marseille into a 37th-minute 1-0 lead, and Kevin Theophile-Catherine levelled for Rennes after 59 minutes.
Marseille midfielder Joey Barton wrote on Twitter: "Absolutely gutted. Feels like we've lost today. Should of [sic] been a well deserved 3pts."
Marseille stay third in the table, now level on points with Paris St Germain who will have the chance to join front-runners Lyon on 45 points when they play Lille tomorrow.
Rennes, meanwhile, remain fourth, six points behind Marseille and PSG.
Montpellier moved into seventh place with a 2-0 win over Sochaux thanks to goals by Emanuel Herrera, in the 28th minute, and John Utaka, who netted six minutes later.
At the other end of the table, Nancy won in the league for only the second time this season when they beat Lorient 2-1.
Paul Alo'o Efoulou opened the scoring for the league's bottom side nine minutes before half-time. Although Jeremie Aliadiere equalised five minutes after the break, Nancy were not to be denied and Sebastien Puygrenier hit the winner after 71 minutes.
It was Nancy's second win this week after they defeated Nice in the Coupe de France in midweek, however they still prop up the table after second-bottom Troyes beat Brest 2-1.
Fabien Camus and Stephane Darbion scored after 44 and 54 minutes respectively to give hosts Troyes a two-goal lead, and although Eden Ben Basat pulled one back in the 61st minute Troyes held on for their third league victory of the season.
Third-bottom Reims drew 1-1 with Toulouse. Etienne Capoue put Toulouse ahead after 56 minutes with Grzegorz Krychowiak levelling with a little over quarter of an hour remaining.
Evian, fourth from bottom, were matched 1-1 by Ajaccio. Dennis Oliech put Ajaccio ahead after 36 minutes before Daniel Wass levelled for the hosts in the 53rd minute.