Benedetto and Germain scored after halftime to put OM on 24 points from 11 matches, one behind leaders Paris Saint-Germain who have played one game more.
Nimes were reduced to 10 men in the 77th minute after Andres Cubas was sent off.
They lie 16th in the standings on 11 points from 13 matches.
Andre Villas-Boas's side dominated possession and played neatly, but Nicolas Eliasson came closet for the home side in the 17th minute when his curled 25-metre shot crashed onto Steve Mandanda's crossbar.
Villas-Boas was sent off after protesting against the referee's decision to hand a yellow card to defender Duje Caleta Car for a rough tackle, five minutes before the break.
OM continued to dominate in the second half and after a couple of missed chances, Benedetto found the back of the net with a delicate chip after being played through by Alvaro Gonzalez.
Hopes of a Nimes comeback were dashed in the 77th minute as Cubas was sent off following a second bookable offence.