Bernardo Silva sent Pep Guardiola's side ahead in the 26th minute, before Newcastle turned the game around late in the first half courtesy of goals from Alexander Isak and Anthony Gordon.
De Bruyne, on his return to league football after recovering from a long-term hamstring issue, then made it 2-2 in the 74th minute, before the Belgium international set up Oscar Bobb, with the 20-year-old's first Premier League goal securing all three points for the Citizens in the final exchanges.
The result has moved Man City into second spot in the table on 43 points, just two points behind the leaders Liverpool, while Newcastle stay 10th, boasting 29 points from their opening 21 matches of the campaign, and the Magpies have now been beaten in their last four league fixtures.
Newcastle thought that they had taken the lead inside the opening two minutes when Sean Longstaff turned a low Isak cross into the back of the net from close range, but the offside flag was raised shortly after, with VAR confirming that it was the right call.
Man City goalkeeper Ederson was actually injured in the resulting collision with Longstaff, with Kyle Walker also in close proximity to his teammate, and the Brazil international needed a period of treatment before the play continued in the fifth minute.
Ederson's first touch after the clash was a poor one, and it almost cost Man City a goal, but Walker's pace got the champions out of trouble, with Bruno Guimaraes's swing of the boot dealt with by the England international.
The Man City stopper immediately dropped to the ground, and it became clear that a substitution would need to be made, with a limping Ederson replaced by the club's number two Stefan Ortega.
Newcastle had another half-chance in the 16th minute when Miguel Almiron delivered into Isak, but Ruben Dias just about did enough to make the challenge, before Bernardo fired over down the other end following a quick counter-attack from Guardiola's side.
Jeremy Doku then had a shot deflected wide in the 19th minute, and the pressure was building, with Man City making the breakthrough in the 26th minute courtesy of a wonderful goal from Bernardo.
Walker delivered a brilliant cross into the Newcastle box, and Bernardo flicked the ball into the bottom corner with a quite stunning finish to silence the home supporters; Newcastle wanted a free kick some 54 seconds before the goal, with Dias bringing Gordon to the ground, but the goal was allowed to stand.
Newcastle goalkeeper Martin Dubravka pushed a strike from Bernardo onto the crossbar in the 29th minute, before Josko Gvardiol fired over the crossbar moments later.
A mistake from Ortega presented the home side with a chance in the 32nd minute, but Rodri came across to deny Isak, who continued to look the most likely for Eddie Howe's side, before Dubravka had to keep out a strike from Julian Alvarez down the other end of the field.
The response from Newcastle came in the 35th minute, with Isak expertly curling the ball into the far corner of the net after a wonderful pass from Guimaraes had released his teammate.
The Magpies incredibly then took the lead in the 37th minute, and it was another wonderful goal, with Gordon working the ball into his right foot before curling it past Ortega in almost a carbon copy of Isak's effort.
Ortega did well to deny Isak in the 41st minute, with the Newcastle forward causing all sorts of problems due to his pace and movement, and a pulsating opening half of action ended with the home side 2-1 ahead.
Alvarez brought a smart save from Dubravka early in the second period, with the Argentina international looking to pick out the corner from a free kick, before the Newcastle goalkeeper denied Phil Foden in the 58th minute.
Man City were on the front foot, with the Citizens passing and probing in the final third of the field, but they were struggling to create clear openings, with Foden firing over the crossbar from distance on the hour.
The visitors had another chance in the 62nd minute, with Walker's incredible pace taking him into the Newcastle box, but there were no takers on the right-back's low cross, with the ball just behind Foden.
Dubravka kept out another strike from Alvarez in the 64th minute, before Ortega did well to beat Isak to a Dan Burn cross down the other end, with both teams threatening to score the game's fourth goal.
Mateo Kovacic had a strike deflected into Dubravka's arms in the 68th minute, before Alvarez somehow fired over the crossbar from inside the box, shortly after De Bruyne had been introduced for his first Premier League appearance since August.
De Bruyne did not take long to make his mark, with the Belgium international passing the ball into the bottom corner of the net in the 74th minute to make it 2-2 after a brilliant pass from Rodri had released him in a dangerous area.
Gordon had a shot deflected wide of the post down the other end in the 79th minute, but Man City were dominating the ball against their tiring opponents, with the champions waiting for the moment to pounce.
Dubravka kept out a curling strike from Rodri in the 84th minute, but the visitors won it in stoppage time, with substitute Bobb collecting a sensational pass from De Bruyne and finishing into the back of the net after showing incredible feet in a tight area.
Both teams will now enter a winter break, with Man City returning to action against Tottenham Hotspur in the fourth round of the FA Cup on January 26, before Newcastle take on Fulham in the same competition on January 27.