Earlier in the evening Bordeaux beat Monaco 3-0 while Lyon won their last ever game at the Stade Gerland, 2-1 over second-tier Tours.
Paris coach Laurent Blanc rotated his side, who drew a home tie with Lyon in the quarter-finals, and Italian goalkeeper Salvatore Sirigu was acclaimed by the crowd as he made only his second start of the season after being displaced by newly arrived German stopper Kevin Trapp.
PSG's record goal-scorer Zlatan Ibrahimovic almost added to his collection of spectacular strikes when hitting the woodwork with a scissor-kick in the opening period.Â
The Swede looked disgruntled when he made way for Angel di Maria after an hour, but it was a decisive switch.
Di Maria teamed up with fellow sub Cavani to grab the winner after a fine pass and finish in the 86th minute of a tight game as Paris went all out for a goal to avoid extra-time and penalties.
And Cavani's left-foot volley was as beautiful as Di Maria's defence splitting lob that found the Uruguayan running full-pelt into the area before curling a deft shot past Jessy Moulin in the Saint Etienne goal.