Cavani scored from the spot, adding to Thiago Silva's opener to round off a win for the Parisians, who trail Nice by a solitary point after the Cote d'Azur table-toppers handed Guingamp a first home defeat.
Uruguayan Cavani's big moment came after Hatem Ben Arfa strode forward on a mazy run only to be brought down by Romain Thomas.
The goal machine, having made it 19 goals in 18 matches so far this season, promptly earned a booking for taking off his shirt to reveal a T-shirt slogan paying homage to Brazilian side Chapecoense, the club decimated by an aircrash in Colombia.
Cavani joined PSG from Napoli in 2013 for a French record fee of 64 million euros ($67.8m) and now is the club's fourth top goalscorer -- now just one adrift of Dominique Rocheteau.
Out in front with 156 is Zlatan Ibrahimovic, who left for Manchester United last summer.
"It was a very important match, for the three points, for the table because we were at home and it was important to be strong for the fans," said PSG coach Unai Emery.
"Against a very defensively compact team, we put in a solid performance."
Moroccan Younes Belhanda bagged the only goal for Nice, this season's surprise package, in the fifth minute with a sumptuous strike from the edge of the box.
Nice won in the absence of the injured Mario Balotelli, who has a calf problem.
The southerners badly missed Balotelli in their weekend draw with Bastia but on loan Dynamo Kiev star Belhanda's effort was enough to drag them over the line, to the relief of coach Lucien Favre.
"We knew it would be tough to take the points here," said Favre.
"Having got the first goal we didn't manage to get to 2-0. If you don't then you have to hold on to what you have -- and we did that.
"Everyone must pull together. There is a fine margin between success and failure."
Nice will meet PSG just before the Christmas break and Favre said that encounter would be crucial -- albeit they are not looking that far ahead.
"If we take the three points in that one then all well and good. (But) beforehand we have Toulouse, who are a tough opponent. May I remind you they are the only side to have beaten both Paris SG and Monaco, so that will be a big match."
Monaco, through at the expense of Tottenham to the last 16 of the Champions League, are third, three points off the pace, following their 1-1 draw Tuesday at Dijon.
Lyon stormed into fourth place albeit eight points behind Monaco, with a crushing 6-0 win at hapless Nantes, the eight-times champions, who suffered their worst top flight home reverse.
Nantes are second bottom and staring the droip in the face after an eighth league defeat in 15 games left only Lorient below them.
Nantes coach Rene Girard is hanging onto his job after the Canaries were outclassed with Lyon scoring at will through Corentin Tolisso, an Alex Lacazette penalty, Maxime Gonalons, Mathieu Valbuena, Mouctar Diakhaby and Nabil Fekir.
Marseille stay in midtable after a goalless draw at Saint Etienne in a battle of fallen giants while Bordeaux drew 1-1 at Bastaia, enough to stay in fifth spot ahead of Rennes on goal difference.