Both teams had chances before Antoine Devaux gave Reims a 67th-minute lead, Marseille's response coming through Andre-Pierre Gignac's ferocious strike 10 minutes from time.
The result sees sixth-placed Marseille remain four points outside the European places, even before their rivals take to the field this weekend, while Reims are only one place and one point behind them.
Marseille's sporting director and interim coach Jose Anigo publicly questioned his players' motivation during the week, suggesting several were playing for "individual objectives" in a season which leads into the World Cup in Brazil.
He made only one change to his line-up, Gignac returning from suspension to replace Florian Thauvin, but would have had further reason to doubt his charges after a sluggish start.
Grzegorz Krychowiak was first to threaten for Reims when he let fly from 20 yards and saw his shot skim the outside of a post.
Floyd Ayite's free-kick from out wide then curled dangerously towards goal, forcing Steve Mandanda into a scrambling save.
Dimitri Payet's free-kick, beaten away by goalkeeper Kossi Agassa, was an isolated Marseille threat until they stepped up their efforts just before half-time.
First Benoit Cheyrou stung the hands of Agassa with a fierce right-foot shot before another Payet free-kick curled against the outside of the post and away to safety.
Gignac served notice of his threat with a thunderous volley shortly before the hour mark, but found Agassa equal to it down low.
But Ayite and Nicolas de Preville each drew sharp saves from Mandanda before Reims' breakthrough eventually came.
Full-back Franck Signorino was the architect of the goal, bursting down the right flank before crossing for Devaux to head superbly past Mandanda.
Payet's effort shortly afterwards was charged down but Marseille continued to push and their equaliser arrived when Andre Ayew turned Rod Fanni's cross into the path of Gignac, whose first-time shot was too powerful for Agassa.
There was still a late threat to OM's goal as Gaetan Courtet set up Devaux, but Mandanda blocked on the line to preserve a point.