After a nightmare start, the Magpies found themselves 3-1 up early in the second half thanks to goals from Miguel Almirón, Callum Wilson and Kieran Trippier, only for City to fight back and claim a share of the spoils.
United fell behind inside the opening five minutes, with Ilkay Gündogan afforded time and space in the box to become the first player of the season to find a way past Nick Pope.
And the Magpies were grateful to the England goalkeeper for two big saves with his feet to keep his side in the game - the first from Kevin De Bruyne in the tenth minute, following a City counter-attack, the second from Phil Foden six minutes later.
But Newcastle began to find their feet from there, with Allan Saint-Maximin leading the charge. In the 17th minute, he flashed a low cutback from the left across goal then, when the ball found its way back to him, the Frenchman pulled the ball back for Almirón, who blazed over.
Pope then made another vital save, diving full length to keep out De Bruyne's free kick, and Newcastle broke, with Almirón firing in a low delivery which nobody was able to force home.
Then Saint-Maximin jinked into the box and saw his shot parried away by Ederson, before Wilson had an effort deflected wide.
But Almirón - the subject of a Wor Flags banner in the Gallowgate End as the teams took to the pitch - equalised in the 28th minute. He got a touch to Saint-Maximin's cross and although the flag initially went up for offside, VAR intervened to spark jubilant scenes inside the ground.
And the majority of the 52,258 crowd were celebrating again 11 minutes later when Saint-Maximin slid in Wilson, whose first touch set him up for a clinical second as he fired beyond Ederson.
Pope made a comfortable save in the 43rd minute, dropping to his left to hold Rodri's long-range shot, before, on the stroke of half time, Fabian Schär appeared to be brought down in the box by a clumsy John Stones challenge, but the VAR officials opted against getting involved for a second time in the space of a few minutes.
The visitors came out strongly at the beginning of the second half, with Pope making another superb save to push Erling Haaland's shot onto a post. But United immediately countered, and when the livewire Saint-Maximin was felled on the edge of the box by Stones, Trippier, who started his career with City, stepped up to whip a delicious free kick arcing beyond Ederson and into the Gallowgate net.
City, though, are champions for a reason, and pulled one back on the hour through Haaland, who blasted in his third goal of the season from close range.
The Norwegian nearly had another when he wriggled clear of Sven Botman, but Pope was off his line in a flash to block at his feet.
City were quickly back on level terms, however, when Bernardo Silva swept home from a threaded De Bruyne pass to make it 3-3.
In the 74th minute, Trippier was harshly shown a straight red card for a foul on De Bruyne inside the City half, but referee Jarred Gillett overturned his hasty decision after being advised to check the VAR monitor.
And although City pushed for a winner in the closing stages, it was actually Newcastle who came closest when Dan Burn nodded Trippier's corner towards Botman, but the Dutch defender volleyed over the bar.
