Cyprien capped off a fine team move with a thunderous effort from 25 metres in the seventh minute as Nice bounced back from Saturday's 3-0 defeat at Monaco.
Although Lucien Favre's side were unable to add to their tally, they were not troubled by a lethargic St Etienne and stayed third in the standings on 52 points after 24 matches, level with Paris St Germain and three behind leaders Monaco.
Elsewhere, troubled Olympique Lyonnais delivered the perfect response after last weekend's derby defeat by St Etienne and ended their three-game losing streak by thumping Nancy 4-0 at home, new signing Memphis Depay completing the rout with his first goal for the club.
Marseille moved up to sixth on 36 points by beating Guingamp 2-0 at home, Dimitri Payet marking his first start since his 25 million-pound ($31.4 million) move from West Ham United with the hosts' second after Bafetimbi Gomis grabbed the opener.
(Reporting by Ed Dove, Ed Osmond)
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