Dembele who just returned from a loan at Atletico Madrid found the back of the net after some nice work in the area by Lucas Paqueta as Peter Bosz's team moved up to sixth with five points after four games.
They finished with 10 men after Damien Da Silva was sent off 12 minutes from time but showed some defensive steel to grab all three points.
Nantes, who had chances before halftime, are 10th on four points.
Lyon went ahead on 35 minutes after Paqueta's strike was parried by keeper Alban Lafont into the way of Dembele, who poked the ball home to give the visitors a deserved advantage.
Jean-Charles Castelletto came close to equalising two minutes later but Anthony Lopes pulled a brilliant save to maintain Lyon's lead.
The Portuguese keeper was at it again just before halftime when he tipped Sebastien Corchia's free-kick over the bar.
Lyon controlled the second half although they had a scare in the closing stages after Da Silva picked up a second yellow card for elbowing Ludovic Blas.
Leaders Paris St Germain travel to Reims on Sunday with new signing Lionel Messi expected to make his Ligue 1 debut.