Nantes were promoted to France's top flight last season, and have enjoyed a fine season thus far.
That continued at the Stade Velodrome on Friday, as Marseille were condemned to a second straight defeat after an agonising 1-0 loss to Lille on Tuesday.
Baup's side failed to find any fluency in the opening exchanges and trailed at half-time thanks to Alejandro Bedoya's third goal of the season - and second this week - on 16 minutes.
Marseille almost fell two behind when Papiss Mison Djilobodji headed towards goal from a corner, but Steve Mandanda produced a smart reflex save.
The hosts improved after the break with Florian Thauvin and Andre-Pierre Gignac coming close.
Yet they were unable to find an equaliser, much to the chagrin of the home faithful, and remain 10 points adrift of table-toppers Paris Saint-Germain having played a game more.
