City took the lead inside five minutes but Newcastle turned it around before the break with goals from Almiron and Wilson.
Trippier whipped in a brilliant free-kick to make it 3-1. City rallied quickly and two goals in four minutes from Haaland and Silva brought them back level.
Kieran Trippier provided a sublime free-kick to give Newcastle a deserved 3-1 lead early in the second half against the champions
Silva was making his first start of the season and crossed from the right flank for Gundogan to score for the second time in as many matches
Liverpool face bottom of the table Manchester United on Monday with neither side having managed a win so far.