After beating Toulouse twice in Ligue 1 and in the French Cup this month, PSG left it late to subdue the visitors and set up a final clash with Lille who knocked out Girondins Bordeaux 5-1 on Tuesday.
Coach Laurent Blanc fielded a largely reserve side with key players Zlatan Ibrahimovic, Thiago Motta and Blaise Matuidi on the bench.
PSG, who won the last two League Cups, were too clumsy in the first half, giving Toulouse with hope of an upset at the Parc des Princes.
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But Lavezzi, who has only started three league games this season, fired home at the second attempt in the 65th minute after keeper Mauro Goicoechea failed to deal with the Argentine’s first strike.
Di Maria wrapped it up seven minutes later with a 20-minute floating shot into the top corner as PSG stayed unbeaten in domestic competitions this season, firmly on course for a second successive domestic treble.
The League Cup final will be played at the Stade de France on April 23.
(Reporting by Julien Pretot, editing by Ed Osmond)
