Three days after the two teams played out a dull 0-0 league draw, they put on a much more entertaining spectacle.
PSG, however, never looked under threat and recorded a morale-boosting victory ahead of next week's Champions League last-16 return leg against Chelsea.
Centre back Luiz headed home from Ezequiel Lavezzi's free kick in the third minute as PSG made the perfect start against Monaco, whose coach Leonardo Jardim had made seven changes from the team who played on Sunday.
They doubled the lead seven minutes into the second half, with Marco Verratti setting up Cavani in the penalty area to beat Maarten Stekelenburg with a low shot. PSG continued to dominate and Javier Pastore and Cavani both hit the woodwork.
Monaco, who beat Arsenal 3-1 at the Emirates Stadium in their Champions League last 16 first leg last week, were never in contention and seemed short on ideas as they struggled for a foothold in the final 10 minutes.
St Etienne reached the last four on Tuesday by beating third division Boulogne on penalties.
Stade Brest take on Auxerre in an all Ligue 2 clash and amateurs Concarneau, who play in the fourth division, host Guingamp on Thursday.
(Reporting by Julien Pretot; editing by Toby Davis)
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