Uruguay striker Cavani was his usual wasteful self in the first half, missing a couple of chances, until he found the net in the 57th and 73rd minutes to put PSG on a maximum 12 points from four games.
Ezequiel Lavezzi added a third seven minutes from time after being perfectly set up by fellow Argentine Angel Di Maria, who was impressive on his debut after joining PSG from Manchester United during the close season.
Laurent Blanc's side lead Stade de Reims by three points while Monaco, who were eliminated in the playoff round of the Champions League by Valencia earlier this week, are 13th on five points.
PSG, who have yet to concede a goal this season, started with Zlatan Ibrahimovic up front as the Sweden striker made his Ligue 1 season debut after recovering from a knee injury, with Di Maria started on the bench.
Cavani sent a header over the bar and miscued a shot on the stroke of halftime as PSG dominated possession but failed to really unsettle a solid Monaco defence.
Cavani eventually opened the scoring with a header at the near post from Blaise Matuidi's cross.
He made it two 16 minutes later with a low shot after being set up by Ibrahimovic.
In the 83rd, PSG put the hammer down when Lavezzi collected Di Maria's defence-splitting pass from his own half before firing past Subasic from inside the box.
(Reporting by Julien Pretot; Editing by Mitch Phillips)
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