The Georgia winger joined from Napoli for a reported 70 million euros ($A115 million) and with a big reputation for skill and clinical finishing.
He showed a bit of both in the 54th minute, controlling a quick pass with his right foot, cutting cleverly inside Christian Mawissa and scooping the ball off balance over goalkeeper Radoslaw Majecki.
That made it 2-1 and, three minutes later, Ousmane Dembélé added the third goal after combining well with Désiré Doué. He tapped in from close range in the last minute following a counterattack to extend his league-leading tally to 16 goals.
PSG led in the sixth minute when Vitinha curled a free kick into the bottom right corner. But he was helped by a major positional error from Majecki, who left a huge gap.
PSG goalkeeper Gianluigi Donnarumma was easily beaten at the near post when captain Denis Zakaria ran onto a smart pass from Soungoutou Magassa.
For all its attacking flair - especially the technically gifted Maghnes Akliouche - Monaco's weaknesses were poor composure and erratic defending, and will drop to fifth if Lille and Nice win this weekend.
Marseille will stay second regardless but must win at Angers on Sunday to remain 10 points behind PSG, who announced they had renewed the contract of coach Luis Enrique by two years to 2027.
The former Barcelona and Spain coach arrived in 2023 and is overseeing a new team strategy after the end of the era of superstars like Kylian Mbappe and Lionel Messi.
"I'm very happy to continue this story with Paris Saint-Germain," he said.
"I feel very comfortable here; we have all that we need in order to work in the best possible conditions. I think that the future looks very bright, and I hope to enjoy a lot more success with the club."
PSG also confirmed Achraf Hakimi, Vitinha and Nuno Mendes have all been tied to the club now until 2029, and Yoram Zague until 2028.
Earlier, imposing striker Ludovic Ajorque and midfielder Pierre Lees-Melou scored as Brest won at Nantes 2-0 to climb into seventh spot.
Nantes' three losses in their last 11 games have all been against Brest - with the other in the French Cup.
Brest will host PSG on Tuesday in the first leg of their Champions League playoff match.
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