Lucien Favre's side, who have proved to be the surprise package of the league, scored the game's only goal when Eyserric was gifted possession on the edge of the area before he dispatched an unstoppable effort beyond Stephane Ruffier in the St Etienne goal.
The hosts had a strong claim for a penalty when defender Dante appeared to handle inside the area, but the referee waved the claims away as Nice responded from their defeat at Caen before the international break.
Jimmy Briand's stoppage-time equaliser helped Guingamp salvage a 1-1 draw against Bordeaux at the Stade du Roudourou.
Bordeaux took the lead after 23 minutes when Igor Lewczuk headed home Valentin Vada's free-kick. The visitors could have secured all three points with 12 minutes left after Guingamp midfielder Lucas Deaux conceded a penalty. But Karl-Johan Johnsson saved Jeremy Menez's spot-kick to give Guingamp a lifeline.
In the fifth minute of stoppage-time Deaux made up for his error when he set up Briand to head past Bordeaux goalkeeper Jerome Prior and keep Antoine Kombouare's team in fifth place in Ligue 1.
Rolando's goal eight minutes from time helped Marseille to a 1-0 win over Caen at the Stade Velodrome.
The defender was left unmarked in the box to nod in a cross from Bafetimbi Gomis as Marseille climbed up to 11th with the win.