The Brazilian, one of the best PSG players this season, opened the scoring from inside the box before the interval and set up Argentine Javier Pastore for the second after the break.
He put the result beyond doubt in the 68th minute with a solo goal to give PSG 43 points from 20 games. Daniel Braaten scored a consolation goal for the visitors in the closing stages of a lively match.
PSG still lead Montpellier by three points after the Southerners beat Olympique Lyon 1-0 courtesy of an Olivier Giroud second-half goal.
At the Parc des Princes, Ancelotti shook things up, leaving France striker Kevin Gameiro on the bench to field Jeremy Menez, who usually plays on the wings, alone up front.
Full-back Maxwell, who joined from Barcelona two days ago, also featured in the starting XI and was barely tested throughout.
It took PSG, who have not won the French league since 1994, more than half an hour to settle but Nene broke the deadlock in the 38th minute with a deflected shot from the spot.
The home side then played more freely and Nene set up Pastore with the Argentine playmaker, who joined for a French record 42 million euro fee last summer, slotting past Ali Ahamada shortly before the hour.
Nene then raced down the right flank before beating Ahamada with a fine angled shot to wrap up a straightforward win.
"we would have liked not to concede. But it's a good win, we played very well from start to finish," captain Mamadou Sakho told French TV channel Orange Sport.
"We made a lot of efforts but if we continue like this we will many more games."
Montpellier struggled against Lyon but Giroud's 14th goal of the season was enough to secure the win. France striker Giroud fired home with an angled shot at the end of a sharp counter-attack as Montpellier kept their title challenge on track.
"It was a solid game from us. We deserved our victory," Montpellier coach Rene Girard told a press conference aired by French TV channel Infosport.
Stade Rennes stayed fifth on 35 points when goals by Jires Kembo-Ekoko and Victor Hugo Montano gave them a 2-0 win at Caen.
