Second-placed PSG, who have three games to play, were left three points behind leaders AS Monaco who also have a game in hand. Nice trail PSG by another three points in third.
Mario Balotelli and Ricardo Pereira scored to put Nice 2-0 ahead before Marquinhos pulled one back. Anastasios Donis scored Nice's third in the 90th minute, in between red cards for Thiago Motta and Angel Di Maria.
Tempers had flared several times before that, with PSG forward Edinson Cavani in the thick of the trouble.
Nice went ahead in the 26th minute after Ricardo Pereira broke out of his half and charged down the right.
He seemed to have run into a dead end but turned back and laid the ball off to Balotelli, who held off Marco Verratti and curled a low shot under Kevin Trapp's hands and into the corner from 20 metres for his 14th goal of the season.
Shortly afterwards, there was a flare-up when Paul Baysee and Cavani tangled in the Nice penalty area but the referee let the feuding pair off with a warning.
Read the full article on eurosport.co.uk: PSG's title hopes dented in stormy defeat at Nice