Nice were missing suspended striker Mario Balotelli but still created plenty of chances either side of Eysserick's clinical 63rd-minute strike into the top corner from 15 metres.
There were muted celebrations by the 24-year old midfielder, who spent last season on loan at St Etienne, scoring six league goals in 29 games before returning to Nice in the close season.
Nice striker Alassane Plea missed two easy chances within minutes shortly after Eysseric scored and Jean Michel Seri also twice came close in the first half, with St Etienne's Stephane Ruffier making several fine saves.
The keeper pushed over a spectacular Younes Belhanda lob from the halfway line deep into stoppage time moments after the hosts had missed a great chance to equalise when Loic Perrin blasted the ball over the bar from five metres.
(Writing by Zoran Milosavljevic; Editing by Ken Ferris)
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