Despite Nice making the better start, it was the home side took the lead in the 27th minute. A cross from the right was pulled back to Serge Gapke before his first-time side-footed effort was pushed wide by Mouez Hassen in the Nice goal but straight into the path of Djordjevic, who tapped in from three yards out.
It was the home side who dominated after the break and had a number of chances to go further in front, firstly through Veretout, but he shot straight down the throat of Hassen.
Nantes squandered another opportunity with 25 minutes to go when Djordjevic nodded the ball down into the path of Vincent Bessat, but his shot flew wide across the face of goal.
However, Nantes finally sealed the win a minute from time when Aristeguieta powerfully headed home a cross from the right at the near post.
Nantes climb up to ninth while Nice drop to seventh in the table.