Everson was the scourge of the Principality side, as he netted the only goal of the game and caused untold problems for Didier Deschamps` charges.
The deciding goal came on 24 minutes when Everson showed great awareness to control a ball and fire past Tony Sylva from the edge of the box after his initial free-kick cannoned back off the wall.
Monaco pressed hard for an equaliser, and created chances but had little in the way of cutting edge to trouble Nice keeper Damien Gregorini.
It was Nice who had the only other goalscoring opportunity, but Kaba Diawara`s strike from close range was disallowed for offside, after Sylva could only parry a fine shot from the impressive Everson.
