Second consecutive victory for the Eagles, who went on to win 5-4 in Épinal.
Despite never having led in this match, the team from Nice waited until the last minute to take an advantage that they managed to hold onto until the end.
Nice joins Épinal in the standings and can now hope to move out of the bottom four places, which would mean avoiding the relegation group at the end of the season.
The Eagles will host Mulhouse (10th) in the next round.