Angers, the competition's surprise package of the season, took a first-half lead through Pierrick Capelle before Ben Arfa ended his 10-game goal drought with a pair of successful spot-kicks in the final 11 minutes.
Angers - who remain in second place despite the defeat - had little possession in the first half yet still they entered the interval with a 1-0 lead through the lively Capelle.
An early warning sign appeared in the 16th minute when Charles Diers floated in a pinpoint cross from the left.
Capelle had ghosted unmarked into the area but his goalbound header was well saved by keeper Yoan Cardinale.
Cardinale could do nothing to stop Capelle in the 24th minute, however, after a long pass by Romain Saiss caught Nice's defence off guard.
Two brilliant touches and a cool finish later and Capelle had driven Angers into the lead.
Nice drew level in the 80th minute after a controversial penalty that saw Ben Arfa fall after appearing to get his leg tangled with Ismael Traore. Ben Arfa sent keeper Alexandre Letellier the wrong way and Nice were level.
Three minutes later they snatched the lead when Vincent Manceau handled Niklas Hult's cross and Ben Arfa stepped up to deliver the winning goal as Nice moved into the top three, a point behind Angers.