The first half was a tight affair that saw few goalscoring opportunities for either side, with perhaps the best of the lot falling to Kevin Monnet-Paquet, who dragged his effort into the arms of Benoit Costil.
The first real chance of the match finally arrived 10 minutes into the second half when Jeremie Boga found himself with space to shoot inside the area, but he lacked composure and side-footed his effort over the crossbar.
Saint-Etienne responded with their most threatening moment of the match up to that point as Bahebeck tested Costil and Florentin Pogba's overhead kick from the resulting corner flew narrowly wide of the target.
It was the visitors who were having the more shots on goal, and one of them finally paid off with a little over 15 minutes remaining in the match when Moustapha Bayal Sall towered over everyone at the back post to plant a firm header past Costil.
The hosts went in search of an equaliser and very nearly got one five minutes later when Giovanni Sio collected the ball in a promising area, only to fluff his lines and scuff an effort wide.
Pogba was also called upon to thwart a close-range effort from Kamil Grosicki, but Saint-Etienne held out for the victory to leapfrog their opponents in the table and move within one point of the top four.