The French champions face Evian on Wednesday knowing that their newly promoted title rivals now sit just two points behind them in Ligue 1.
Claudio Ranieri's men made it three wins in a row without conceding a goal after James Rodriguez, Emmanuel Riviere and Lucas Ocampos found the target.
The victory means Monaco moves to just two points behind PSG, which travels to face Evian on Wednesday, at the top of the French standings having played one game more than its title rival.
Monaco was once more without the injured Radamel Falcao but took just five minutes to open the scoring, with the striker's compatriot Rodriguez curling in superbly from a tight angle.
The visitors doubled their advantage midway through the half when Riviere met young Anthony Martial's cross to steer a looping header inside the post.
Danijel Subasic denied Dario Cvitanich just a few minutes later as Nice fought for a way back into the match, before Riviere sent a chip over the crossbar.
Riviere then spurned a great chance for a third just after the break, tumbling at the vital moment after skipping around Nice goalkeeper Luca Veronese.
Nice continued to battle but couldn't find a route back into the match and, in the 89th minute, Ocampos made the points safe, robbing Mathieu Bodmer and rounding Veronese before slotting home.