Lucien Favre's Nice team were missing their top scorer Mario Balotelli but Plea stepped up with a clinical finish in the 61st minute, latching onto Valentin Eysseric's cross to score the only goal of an otherwise rather dull encounter.
Unbeaten Nice have 17 points from seven games and lead AS Monaco, who beat Angers 2-1 on Saturday, by one point.
"It was not easy, we knew it would be tough," said Nice midfielder Remi Walter. "We are reaping the rewards from our efforts in training. It does not mean much, however, to lead after only seven games."
The visitors had to cope without Balotelli after the Italian striker, who has already netted four goals in Ligue 1 this season, was ruled out with a groin injury.
They sat back in the first half but made the most of their best chance when forward Plea connected with Eysseric's chipped pass to score his third goal of the season.
St Etienne moved up to seventh place on 12 points with a 3-1 victory at home to bottom club Lille, who have four points.
Nancy are second from bottom on five points.
Champions Paris St Germain are four points off the pace in fourth spot after a 2-0 defeat on Friday at third-placed Toulouse who are a point above them on 14.
(Reporting by Julien Pretot; Editing by Ken Ferris)
