Marseille cut the gap to Ligue 1 leaders Lyon to a single point thanks to their late 2-1 win over Guingamp on Sunday.
Mario Lemina opened the scoring for L'OM in the 84th minute before Andre-Pierre Gignac added the hosts' second in the 89th.
Marseille looked to have wrapped up the game and even Claudio Beauvue's 92nd-minute penalty and the sending off of Rod Fanni was not enough to stop the Stade Velodrome side from claiming all three points.
OM moved clear of Paris St Germain to sit second with 44 points after PSG has earlier moved level thanks to a 4-2 win over Evian.
Marseille began on the front foot, dominating early possession, but it was the visitors who had the best chance in the opening 15 minutes when an unmarked Younousse Sankhare headed straight at Steve Mandanda from six yards.
L'OM responded and, when Andre-Pierre Gignac rose highest from a free-kick, his header seemed destined for the back of the net until the stretching Jonas Lossl got a superb hand to turn the ball around the post.
Despite struggling early on, Guingamp began to grow in the match and went agonisingly close on two occasions before the interval.
Firstly, Beauvue's teasing cross found Sankhare at the back post but, after beating Mandanda with his header, the ball came back off the upright much to the hosts' relief.
Then, with the half-time whistle looming, Beauvue broke free on goal but - with just Mandanda to beat - the Guadaloupe-born midfielder lacked the required composure and blazed over the bar.
The visitors were given a let off just before the hour mark when Gignac's acrobatic effort appeared to hit the raised hand of Dorian Leveque inside the area but referee Wilfried Bien remained unmoved, much to the displeasure of Bielsa's team.
Both sides continued to create chances with Christophe Kerbrat heading Thomas Thibault Giresse's free-kick over Mandanda's crossbar and Gignac slicing a volley wide of Lossl's goal at the other end, but the opening goal continued to elude both teams.
However, it was Marseille who struck twice late on to break Guingamp hearts when Brice Dja Djedje picked out Benjamin Mendy and, despite Lossl keeping out his effort, Lemima was on hand to head home from close range.
Then, with less than a minute of normal time to play, Dimitri Payet picked out Gignac with a free-kick and the France international did the rest with a well-taken header.
There was still time for Guingamp to make it a nervy finish when Fanni was shown a straight red card for bringing down Beauvue inside the area, who then converted the resulting spot-kick, but it was too little too late for Jocelyn Gourvennec's side.