Le Bihan, who replaced Anastasios Donis just before the hour, struck in the 68th and 86th minutes after Steve Mounie had opened the scoring for Montpellier early in the match.
The victory lifted Nice up to second with 59 points from 27 games, level on points with Monaco but behind the leaders on goal difference.
Third-placed Paris St Germain, who have 56 points, travel to bitter rivals Olympique de Marseille on Sunday while Monaco go to En Avant Guingamp on Saturday.
With first-choice striker Alassane Plea out until the end of the season and the suspended Mario Balotelli also missing, Nice struggled early on.
Mounie put the visitors ahead from close range in the ninth minute after poor defending.
Nice, however, struck back shortly afterwards when Le Bihan, playing his first league game since September, 2015, equalised with a low shot from just outside the box.
A right-foot cross shot from the edge of the area by Le Bihan sealed a deserved victory for Lucien Favre's team.
(Reporting by Julien Pretot; Editing by XXXX)
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