Nivet picked up the ball 25 metres out and unleashed an unstoppable shot to secure a slender advantage for Troyes in their bid for promotion to the top flight.
Lorient, who finished third-bottom in Ligue 1, struggled to create chances in the first half with Troyes looking the more determined side.
The hosts got their reward in the 37th minute with Stephane Darbion tapping the ball in on the rebound after Lorient keeper Benjamin Lecomte saved Nivet's close-range shot.
The visitors came close to an equaliser when Michael Ciani's drilled header forced a reflex save from Troyes keeper Mamadou Samassa, who turned the ball over the bar.
Lorient's Ghanaian forward Abdul Majeed Waris had more luck in the 82nd when he fired home a low shot after Troyes lost possession in their own half before Nivet got the winner.
The teams meet in the return leg on Sunday in Lorient.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
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