Brazilian striker Brandao scored twice while Romain Hamouma and Pierre-Emerick Aubameyang were also on target as the home team netted four times in the opening 25 minutes.
Nancy, who have conceded 14 goals in eight league games this season, are second from bottom. St Etienne are in seventh place with 11 points.
The visitors had Simon Zenke sent off in the 68th minute for a bad tackle.
On Saturday, champions Montpellier host Evian Thonon Gaillard while leaders Olympique Marseille entertain second-placed Paris St Germain on Sunday.