The Uruguayan completed his brace in the 117th minute to give Laurent Blanc's men the hard-earned victory in the last-16 clash at the Parc des Princes on Wednesday.
Cavani had opened the scoring in the 25th minute and PSG looked headed for victory before Mevlut Erdinc levelled in the second half for the seventh-placed Ligue 1 side and defending champions.
PSG were knocked out by Saint-Etienne in the quarter-finals last season on penalties before Christophe Galtier's men went all the way.
Marco Verratti's cross from the left found the 26-year-old free at the back post and Cavani took a neat touch inside to round goalkeeper Stephane Ruffier before placing into an open net.
Lucas Moura almost doubled PSG's lead soon after but was denied by Ruffier before Verratti squandered a decent chance late in the first half.
Substitute Jeremy Menez found space down the right and his pass across the face of goal found Cavani – again left unmarked at the back post – to tap in an easy winner.
Daniel Wass' brace saw Evian TG past Bastia 2-1 and Bordeaux were 2-1 victors at Rennes.
