Monaco sat sixth before the contest, and seven points adrift of PSG - and Thomas Tuchel’s champions looked set to extent that lead after going two goals up in the first half Friday.
Kylian Mbappe struck the first of the night after 25 minutes, and added his second from the penalty spot 12 minutes later to leave Monaco in trouble at Stade Louis II.
Mbappe almost had a first-half hat-trick which would have surely ended the match as a contest, but that strike was ruled out for offside - and Monaco rallied after the break.
Former Arsenal and Chelsea midfielder Fabregas turned the game on its head after coming on at half-time, and Kevin Volland halved the deficit seven minutes into the second half.
Sensing danger, Tuchel brought Neymar on for Angel di Maria at the hour mark - but Volland got his second of the night five minutes later after being assisted by Fabregas.
Mbappe made way three minutes later, and Tuchel was left to rue that decision as Monaco were awarded a penalty nine minutes from time.
Abdou Diallo was initially shown a yellow card for pulling back the influential Volland, but referee Clement Turpin upgraded it to a red card following a VAR review.
Fabregas duly stepped up and converted the spot-kick to complete the fightback, closing the gap on PSG to four points.
The result will put pressure on Tuchel as he seeks to guide PSG out of the Champions League group stages over the next three weeks - and failure there would almost certainly cost him his job.