PSG went 11 points clear at the top of the table and made light of Neymar's absence due to a rib injury by finding an early opener.
Edinson Cavani, back in the side after his unauthorised late return from holiday, laid on the chance for Di Maria, who made no mistake – although the same could not be said when he blazed off target from six yards.
The ex-Real Madrid man and his colleagues were grateful when Emiliano Sala had a header ruled out. Two Nantes players were in offside positions but not involved when a seemingly onside Sala converted.
Claudio Ranieri was entitled to feel aggrieved and his fifth-placed side finished the match with 10 men when Diego Carlos was sent off in bizarre circumstances.
The defender collided with referee Tony Chapron as he charged forward on the break, with the official falling to the ground and appearing to kick out in frustration at Carlos, before regaining his footing and dishing out a second booking for apparent dissent.
Both sides looked sharp and inventive during the opening stages but PSG drew first blood in the 12th minute, with Cavani making his presence felt on his comeback.
The Uruguay striker aimed a precise pass in Di Maria's direction and Kylian Mbappe's exquisite dummy scrambled a Nantes defence appealing in vain for offside, leaving the Argentina midfielder to slot home his seventh goal of the season.