Ferran Torres scored a hat-trick for City and his superb backheeled finish was the highlight of a remarkable game that swung back and forth.
Pep Guardiola, who surprisingly selected Scott Carson in goal - almost a decade on from his last English top-flight game - saw his City side dominate early on but fall behind to Emil Krafth’s powerful header from Jonjo Shelvey’s corner.
Joao Cancelo equalised with a deflected effort into the bottom right corner and when Torres expertly turned home Ilkay Gundogan’s free-kick 185 seconds later it looked as though the visitor could cut loose.
But Steve Bruce, who called upon his Newcastle side to go toe-to-toe with the champion, will have been delighted by its response.
Having been forced to soak up considerable pressure, it levelled when City defender Nathan Ake was deemed to have fouled Joelinton, allowing the Brazilian to score from the penalty spot.
A poorly judged tackle by City full-back Kyle Walker handed the Magpies a second penalty just after the hour mark, with Joe Willock following-up to score after Carson had saved his initial spot-kick.
However, man of the match Torres had the final word, guiding Gabriel Jesus’ cross into the top right corner and then becoming the youngest player to score a league hat-trick for a Guardiola team, when turning in a Cancelo shot that bounced back off the Newcastle post.
Meanwhile on Saturday, Leeds United continued its fine form at the end of its first season back with an impressive victory over Burnley at Turf Moor.
Mateusz Klich curled in from the edge of the penalty area shortly before half-time and Jack Harrison’s flicked finish from Ezgjan Alioski’s strike after 60 minutes all but sealed the three points.
Results: Newcastle United 3 (Krafth 25, Joelinton 45+6, pen, Willock 62) lost to Manchester City 4 (Cancelo 39, Torres 42, 44, 66); Burnley 0 lost to Leeds United 4 (Klich 44, Harrison 60, Rodrigo 77, 79)