PSG, who drew their opening two games, have five points from three matches, and are four points behind arch rivals Olympique Marseille who continued their perfect start to the season with a 1-0 win at Valenciennes on Saturday.
The Ligue 1 champions were cruising in the first half after Uruguay forward Cavani had put them ahead with his second league goal of the season, slotting home after a defence-splitting pass by Zlatan Ibrahimovic in the 24th minute.
But a period of pressure from Les Canaries just before halftime forced PSG keeper Salvatore Sirigu into pulling off two fine saves, including one from a spectacular bicycle kick by Filip Djordjevic.
Nantes continued to test PSG after the break, eventually levelling in the 52nd minute from an inswinging free kick taken by Jordan Veretout that was knocked into his own goal by Brazilian Alex.
Minutes later, Sirigu tipped a header from Alejandro Bedoya over the bar before Argentina's Lavezzi scored PSG's winner in the 73rd minute after a scramble in the box.
Big-spending Monaco lie second with seven points after dropping their first points on Friday in a 0-0 draw at home to Toulouse, while Olympique Lyon, who lost 1-0 at home to Reims on Saturday, are third with six points.
(Reporting by John Irish; Editing by Sonia Oxley)
