Kylian Mbappe had netted a first-half brace, including a penalty, against his former side, taking him to 99 goals for PSG and leaving his current team seemingly on course for a ninth consecutive league win.
But German international Kevin Volland struck twice for Monaco after the break and Fabregas converted from 12 yards in the 84th minute after Abdou Diallo had been sent off for conceding the all-important penalty.
PSG remains clear at the top of Ligue 1, but this result is a major setback for Thomas Tuchel's team before a crucial UEFA Champions League tie against RB Leipzig next week.
Niko Kovac's Monaco climbs up to second in the table, four points behind PSG, but Lille can reclaim second spot and move to within two points of the leader if it beats Lorient on Monday (AEDT).
PSG has been severely handicapped by injuries and suspensions so far this season, and Neymar was only deemed fit enough for a place on the bench at kick-off at Stade Louis II after missing Brazil's FIFA World Cup qualifiers over the last week because of fitness problems.
Mbappe was back in the starting line-up, however, after missing his club's last two outings prior to the international break with a hamstring injury.
Facing his former club, with whom he won the Ligue 1 title in 2017, Mbappe burst through to put Paris in front in the 25th minute after being released by Angel Di Maria.
He then found the net again in the 37th minute, converting a penalty awarded for a foul on Rafinha by Youssouf Fofana.
His ninth goal of the season leaves him just one away from a century of goals in a PSG shirt since his arrival from Monaco at the start of the 2017-2018 season. He even had another goal disallowed just before half-time.
Without France international striker Wissam Ben Yedder after he tested positive for coronavirus, it was a long way back for Monaco but it reduced the deficit seven minutes after half-time when Gelson Martins set up Volland to score from close in.
Volland then equalised with a tap-in after Fabregas, on as a substitute, had beaten goalkeeper Keylor Navas to a cross.
Worse was to come for the visitors, as Diallo – another former Monaco player – clumsily conceded a penalty and was shown a red card after the referee opted to review the images.
Fabregas made no mistake from the spot, smashing the ball home, as PSG lost a Ligue 1 game after leading by two goals for just the second time since the Qatari takeover of the club in 2011.