Unai Emery's star-studded side dominated much of the match against last season's champions, and looked to be cruising to all three points courtesy of goals from Edinson Cavani and Neymar either side of half time.
However, a series of glorious chances to put the game beyond doubt went begging for PSG and in the end they were forced to hang on in the closing stages after Joao Moutinho's free kick had deflected off Kylian Mbappe and into the back of the net.
The result means that PSG remain unbeaten across all competitions this season and have now won their last six outings on the bounce, taking them into a commanding lead over today's opponents at the top of the table.
The visitors should have broken the deadlock inside the second minute when Neymar showed the first glimpse of his dazzling footwork to escape from two defenders and slide an inch-perfect ball through for Mbappe to race on to.
The teenager, who was making his first appearance at the Stade Louis II since leaving Monaco in the summer, beat Danijel Subasic to the ball and took it around the stranded keeper, but could only find the side-netting with the goal gaping.
It should have been a perfect return for Mbappe, and his former club almost punished him for the miss when they had their first half-chance shortly afterwards, but Keita Balde snatched at his effort and blazed it over the crossbar from the edge of the box.
PSG were soon back on the front foot and squandered another glorious opportunity in the eighth minute when Julian Draxler failed to convert Cavani's flick at the back post after Dani Alves and Mbappe had combined down the right flank.
Having missed two near-open goals, PSG eventually broke the deadlock after 19 minutes when Draxler squeezed his cross into the box for an unmarked Cavani, who clipped a smart finish over the keeper from inside the six-yard box for his 16th league goal of the season.
Monaco responded well to going behind, but they struggled to create chances going forward and were limited to only a Radamel Falcao free kick which floated comfortably over the crossbar before half time.
PSG, by contrast, looked capable of scoring almost every time they came forward and nearly doubled their advantage three minutes before the interval when Subasic denied Draxler's effort at the end of a quick counter-attack.
The visitors could comfortably have been three or four up at half time, but instead they were forced to settle for a one-goal lead at the interval and that wastefulness continued in the opening stages of the second half too.
The front three were all queuing up to shoot just two minutes into the match, but both Mbappe and Cavani turned down the opportunity to have a go at goal in favour of setting up Neymar, who crashed his eventual effort against the woodwork.
PSG sliced through their hosts again just a minute later and this time Mbappe had no second thoughts about going for goal, only to see his attempted chip saved by Subasic.
It took a penalty for Emery's side to eventually double their advantage after Almamy Toure clumsily bundled Neymar to the ground inside the area, and the Brazilian took on the spot-kick duties himself to send Subasic the wrong way from 12 yards.
Adrien Rabiot was the next to come close when his powerful drive from just outside the area rose over the crossbar, and from that point on PSG cut Monaco open almost at will in their search for a third goal.
Mbappe was the guiltiest party as the visitors missed a string of gilt-edged chances, first blasting an effort off target under pressure from Kamil Glik when he had Neymar unmarked in support before then clipping a second shot wide of the far post with only the keeper to beat following another defence-splitting pass from Neymar.
Mbappe's return to Monaco would get even worse before the night was through, but prior to that PSG hit the woodwork for a second time when Jemerson turned Cavani's cross against his own post having seen the visitors get in behind the defence yet again.
The profligacy even affected Europe's leading goalscorer when Cavani was left unmarked inside the box just seconds later, only to steer his header wide of the target when he should have scored.
It looked as though PSG's wastefulness in front of goal might come back to haunt them when Monaco pulled one back with just nine minutes remaining as Moutinho's free kick took a deflection off the hapless Mbappe before looping over Alphonse Areola and in.
There was one final chance for the hosts to pull off an unlikely comeback too as Radamel Falcao, who had hitherto been kept quiet by his markers, worked space to shoot but fired his effort straight at the keeper from the edge of the box.
PSG were able to hang on for only their second league win over Monaco for more than a decade, though, increasing their lead over the champions in the process and inflicting back-to-back home defeats on Leonardo Jardim's side for the first time since September 2015.
Monaco (4-4-2): Subasic; Glik, Jemerson, Raggi (Lopes, 62'); Toure, Fabinho, Moutinho, Tielemans (Ghezzal, 67'), Jorge; Falcao, Keita Balde (Sidibe, 79')
Paris Saint-Germain (4-3-3): Areola; Dani Alves, Marquinhos, Thiago Silva, Kurzawa (Yuri, 69'); Verratti, Rabiot, Draxler (Pastore, 82'); Mbappe, Cavani (Di Maria, 82'), Neymar