Cavani netted either side of half-time as Javier Pastore and Angel Di Maria also scored to put the unbeaten capital side on 35 points from 13 games, six ahead of second-placed Monaco after the champions were held to a 1-1 at Amiens on Friday.
Nantes, who are fifth on 23 points, scored through Prejuce Nakoulma as Claudio Ranieri's team faltered under pressure.
The visitors got off to a solid start but cracked before half-time.
Cavani opened the scoring with a clinical finish from inside the box after being perfectly set up by Pastore.
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It was the Uruguay striker's 14th goal after 13 games in the league, the best tally in the French championship since Dick van Dijk with Nice in the 1972-73 season.
Di Maria doubled the advantage three minutes later with a curled cross that nobody could connect with and ended up in the back of the net at the far post.
Nakulma reduced the arrears on the hour mark from close range but Nantes' hopes were short lived.
Five minutes later, Pastore restored a two-goal advantage for the hosts with a powerful shot after being set up by Marco Verratti's through ball.
Cavani put the game to bed 11 minutes from time, poking the ball home from a packed goal-mouth.
(Reporting by Julien Pretot; Editing by Christian Radnedge)
