Veteran Nice midfielder Olivier Echouafni headed an equaliser a minute from full-time to deny 10-man Caen their first league win in 14 outings at the Municipal du Ray.
A horrendous run of form has seen Caen go without a win in Ligue 1 since late November and leave them languishing second from bottom in the table.
It looked like they would finally bring that run to an end when two goals in nine second-half minutes - a Vincent Hognon own goal and Nicolas Seube's strike - shot them ahead after going behind to Loic Remy's sixth-minute opener.
But Caen's task was complicated when they were forced to defend the last seven minutes without Gregory Leca, who was sent off for a second bookable offence, and it proved beyond them as the 36-year-old Echouafni headed in with just a minute to go.
Caen goalkeeper Alexis Thebaux had already reacted well to keep out a deflected Mahamane Traore shot before the hosts went ahead through Remy with six minutes on the clock.
Chaouki Ben Saada made a surging run down the left flank before delivering a cross to the edge of the area where Remy produced a low right-footed shot that beat Thebaux.
Thebaux was easily the busier of the two goalkeepers and scrambled to punch clear a stinging shot from Ben Saada, although it was David Ospina at the other end who produced the best saves of the half when he twice denied Julien Toudic with a couple of reflex stops from close range.
Caen did find an equaliser after 65 minutes when Hognon shinned the ball into his own net under pressure from Sambou Yatabar.
Pablo Barzola had created the danger when he dribbled into space down the right before fizzing in a cross that Hognon failed to deal with.
Nine minutes later Caen were ahead following another defensive lapse.
A poor clearance from Onyekachi Apam allowed Seube the chance to swoop and he took his chance by firing in a right-footed shot from 14 yards to put Caen on the brink of a much-needed win.
But after Leca was dismissed there was an air of inevitability about the arrival of an equaliser and it duly arrived a minute from the end when David Hellebuyck's free-kick into the area found Echouafni to head home.