Both teams were starved of chances in the opening period, with only four shots on goal in total and none on target.
The best of those did fall to heavy favourites Marseille, though, as Mason Greenwood struck over from the edge of the box before Timothy Weah saw a promising effort blocked just before half time.
Auxerre offered very little in attack themselves, but at least showed enough resilience to force what was only the second scoreless first half in 19 Marseille matches.
It did not take long for Marseille to work Donovan Leon in the second half, though, as the Auxerre goalkeeper made a terrific double save.
The first was in response to a Greenwood effort from range, before latching onto the rebound from Pierre-Emile Hojbjerg.
The visitors had survived again, and just prior to the hour mark, Kévin Danois had a chance to put them in front against the run of play, but he blasted over.
Igor Paixao did the same from range down the other end a few minutes later, as Marseille were evidently becoming increasingly frustrated.
However, their persistence paid dividends with just over 10 minutes of the 90 remaining, as substitute Amine Gouiri reacted fastest to a rebound in the area to stab the ball home.
There was as much relief as joy around the Velodrome in that cathartic moment, and Auxerre had no answer as they slumped to a sixth defeat in 11 Ligue 1 games, with just one win to show for during their wretched run.
Their luck truly ran out when Bryan Okoh thought he equalised late on, but his goal was disallowed for handball, keeping the visitors firmly in the relegation play-off spot, while boosting Marseille's prospects of a top-three finish.
Flashscore Man of the Match: Amine Gouiri (Olympique Marseille)
