Bertrand Traore struck the post and Nabil Fekir hit the crossbar, both in the 64th minute, as the visitors failed to make the most of their domination at La Beaujoire.
The result left Lyon in fourth place with eight points from four games, four behind leaders Paris St Germain who have won their four opening games -- most recently beating St Etienne 3-0 on Friday.
Nantes, who have only won one game in the league since Claudio Ranieri took the reins of the first team this season, are 11th on four points.
Nice, third last season, slumped to a 3-0 defeat at promoted Amiens which left the Azurean side in an uncomfortable 16th place on three points after one win and three losses.
Italian striker Mario Balotelli, who was recently criticised by coach Lucien Favre for his lack of dedication on the pitch, missed the trip due to illness.
Dutch playmaker Wesley Sneijder was unable to lift a team who were sunk by a goal from Gael Kakuta and a Moussa Konate double as Amiens celebrated their first victory in Ligue 1.
Girondins de Bordeaux are fifth on eight points after beating Troyes 2-1 while Metz are bottom of the table as the only pointless team following their 1-0 defeat at Caen.