It leaves the English club outside the playoff places and in danger of elimination.
Goals from PSG's Ousmane Dembele, Bradley Barcola, Joao Neves and Goncalo Ramos turned the match on its head, after City had taken the game by the scruff of the neck.
Substitute Jack Grealish and Erling Haaland struck in the 50th and 53rd minutes to give City a 2-0 lead, but fans who braved the torrential rain at Parc de Princes were treated to a brilliant comeback by the hosts.
Dembele latched on to a cross from Barcola to sweep home a goal in the 56th minute. Barcola levelled four minutes later, when he tucked in the rebound after Desire Doue's blistering shot came back off the crossbar.
PSG parked themselves in City's half and took the lead in the 78th minute when the visitors' back line struggled to clear Vitinha's free kick, leaving Neves to head in at the back post and Ramos added the fourth in stoppage time.
PSG climbed to 22nd in the table, while City, who hoisted the Champions League trophy in 2023 but have won just two of their seven group games, dropped to 25th, one spot below the playoff qualification spots.
City's loss sets up a nerve-jangling finale when they host Belgian side Club Brugge next week. The top eight teams qualify automatically for the last 16, while sides finishing ninth to 24th compete in two-legged knockout playoffs to secure their spot in the last 16.
PSG were the better side for most of the game and briefly celebrated a goal by Achraf Hakimi seconds before halftime which was ruled out for offside.
City seemed to be continuing their revival weeks of poor results when Grealish rifled in the rebound from Bernardo Silva's shot, and Haaland doubled the lead when Grealish's cross took a deflection to fall to the Norwegian who hammered home from close range.
But PSG then blitzed the English champions, who had squandered a three-goal lead against Feyenoord to draw 3-3 in November, and they travel to VfB Stuttgart for their final game of the league phase.
Arsenal too classy
Arsenal outclassed Dinamo Zagreb 3-0 to all but secure a spot in the Champions League knockout phase with Declan Rice, Kai Havertz and Martin Odegaard all on target.
Rice struck inside the opening two minutes after a clever lay-off by Havertz and the German put Arsenal in full control with a 66th-minute header.
Captain Odegaard put the icing on the cake of a clinical Arsenal display with a third in stoppage time - his first goal in 14 games in all competitions.
Victory lifted Arsenal to third in the standings on 16 points and with the top eight qualifying automatically for the last 16 only an extraordinary sequence of results in next week's final round of group matches could deny Mikel Arteta's side.
Arsenal travel to Girona for their final game where a draw will be enough to avoid any possibility of being dragged into a two-legged playoff in February.
Defeat for Fabio Cannavaro's Dinamo side left them in the elimination places ahead of their last match at home to AC Milan which they will have to win to stand any chance of a playoff.
Arsenal's Premier League title challenge suffered a blow when they were held 2-2 by Aston Villa at the weekend.
But they have been extremely reliable in the Champions League and a fifth win in seven games was always on the cards once Rice drilled a low shot past Ivan Nevistic after Havertz had cushioned a pass to him from a Gabriel Martinelli cross.
It was Rice's first goal in the Champions League.
Arsenal were occasionally threatened on the counter-attack as Dinamo showed plenty of pace going forward.
Arteta's side began the second half in lacklustre fashion but once Martinelli crossed for Havertz to plant a header past Nevistic the victory was in the bag.
Rice should have added his second when he headed wastefully wide but Odegaard made no mistake late on.
