With the game heading for a penalty shootout, the Uruguay striker came to the rescue with the latest of winners
With Zlatan Ibrahimovic suspended, the Uruguayan stole the limelight and opened the scoring in the first half after good work from Marco Verratti.
However, the game was sent into extra time when former PSG striker Mevlut Erdinc came off the bench to score a late equaliser.
Les Verts have proved a tricky customer for PSG in recent seasons but Cavani's 13th goal in 12 games ensured that it was Laurent Blanc's side who progressed to the quarter-finals.
Chances were few and far between the two sides in a tightly-contested opening 20 minutes with neither goalkeeper being seriously tested.
However, Cavani showed the touch of a man in form on 25 minutes when he controlled Verratti's cross at the back post excellently before taking the ball past Stephane Ruffier and stabbing the ball home.
The Saint-Etienne goalkeeper then produced a magnificent save to palm away Lucas Moura's stinging effort before denying Lavezzi with his legs on the stroke of half-time.
Christophe Galtier's side stole all three points at the Parc des Princes last November and they emerged a much stronger outfit in the second half.
However, it was PSG who continued to have the better of the chances and after Lucas was again denied by Ruffier, Cavani fluffed a golden chance to seal the win after being put through by substitute Javier Pastore.
That miss would prove costly and with 12 minutes remaining, Fabien Lemoine curled an inviting low cross into the box which Erdinc swept beyond Nicolas Douchez to silence the home crowd and send the game into extra time.
With both sides visibly tiring, the match seemed destined for penalties but Cavani had other ideas and justified his expensive price tag by popping up at the back post to tap in Jeremy Menez's cross with just three minutes to play.
Saint-Etienne knocked PSG out of this competition on penalties last term, but there was to be no repeat this time around.