A difficult season for Marseille took another turn for the worse, despite stand-in coach Nasser Larguet naming a strong side for the last-32 encounter.
Jeremy Posteraro gave Canet a 21st-minute lead before Arkadiusz Milik levelled for visitors OM late in the first half.
But defender Yohan Bai scored 19 minutes from time and Canet held on for a famous victory.
Marseille, who sit eighth in Ligue 1, have now only won two of their last 14 games in all competitions.
jc/dj