The result left Nice in 13th place with 29 points from 24 matches.
PSG, who face Barca in their Champions League last-16 first leg on Tuesday, were without three key players with Neymar and Angel Di Maria injured while Marco Verratti was nursing a knock he sustained in a 1-0 French Cup win at Caen on Wednesday.
The Italian was replaced by Draxler, who lived up to the task as he drove the ball home from close range after Mauro Icardi's attempt had bounced off the post into his path in the 22nd minute.
Nice, however, stepped up a gear after the break and Lopes equalised with a powerful shot under the crossbar following a rare poor clearance by Marquinhos.
The visitors went close to taking the lead on the hour but Amine Gouiri's attempt crashed against the bar.
Kean punished them in the 76th minute, heading home from point-blank range to give PSG all three points after Icardi had stretched in the air to deflect Kylian Mbappe's cross.
It was Kean's 10th goal in 17 league games.