The newly-promoted side held their nerves after the Mali international’s second minute strike to record a shocking win at Allianz Riviera.
Doumbia who joined the French side from Rostov for free made his impact felt just minutes into his debut to hand his team a crucial away victory.
He curled in a low shot past goalkeeper Yoan Cardinale after finding enough space outside the hosts’ goal area.
However, he was cautioned in the 23rd minutes by referee Johan Hamel for a foul.
Algeria international Youcef Atta was on from start to finish for Nice but could do nothing in rescuing Patrick Vieira’s side from making a false start in the French elite division.
Reims are seventh in the log and they would be hoping for their first home win of the season when they slug it out against Lyon on August 17.