Metz twice came from behind to equalise before Plea, with his third goal of the game, and Wylan Cyprien struck in the last 10 minutes gave unbeaten Nice their eighth win in 10 league games.
Maverick forward Balotelli, who has enjoyed a revival since his move to the club with five goals in four league appearances, was missing with a thigh injury.
Nice, who have 26 points and are four ahead of Monaco, went ahead after 12 minutes when Jean Michael Seri sent Plea through and the 23-year-old scored with a left-foot shot.
Georges Mandjeck levelled for the hosts but Plea put Nice back in front before halftime from a penalty after a foul on Younes Belhanda.
Metz equalised again through Habib Diallo in the 69th minute only for Plea to put Nice back in front with six minutes left with a shot which went through goalkeeper Thomas Didillon's legs.
Cyprien put the finishing touch when he scored with an angled shot in stoppage time.
Titleholders PSG stayed third but dropped six points behind Nice after their stalemate against Marseille, who are 11th.
(Writing by Brian Homewood; Editing by Ian Chadband and Pritha Sarkar)
