Goals from Raheem Sterling and Bernardo Silva earned the champions all three points in the final match of the opening weekend, condemning Unai Emery to defeat in his first game in charge of Arsenal in the process.
The Gunners struggled to match their visitors for long stages of the contest, although City themselves were not at their scintillating best despite beginning their bid to become the first side to retain the title in 10 years with a routine win.
Pep Guardiola named a City starting lineup missing the likes of Kevin De Bruyne, David Silva, Nicolas Otamendi, Vincent Kompany and Gabriel Jesus, but it did not take long for them to assert their dominance over an Arsenal team clearly still in transition after the exit of Arsene Wenger.
The Gunners came out with clear intentions to start quickly and Aaron Ramsey had one sight of goal inside two minutes which failed to truly test Ederson, but they soon found themselves on the back foot as City showed little signs of a World Cup hangover despite nine of their team having featured in Russia.
Kyle Walker and Sterling in particular were causing problems for the defence, and the latter drew the first save from Petr Cech after only nine minutes when he latched on to Sergio Aguero's pass before turning Shkodran Mustafi inside out and powering a shot towards goal from a tight angle.
It was an ominous warning sign for the Gunners, and sure enough they were behind just five minutes later when Sterling collected possession on the left flank before cutting inside and blasting his finish past Cech from the edge of the box for his 50th Premier League goal.
Opportunities at the other end were few and far between for Arsenal, but the best of the first half fell to Hector Bellerin when he skipped past Benjamin Mendy's challenge to break into the box, only to blast his effort too close to Ederson.
City were immediately back on the front foot, though, and Aguero fired one effort into the side-netting before Cech - selected ahead of summer signing Bernd Leno in goal - almost passed the ball straight into his own net when trying to play out from the back.
It was not the only moment of uncertainty in possession for the veteran shot-stopper, but he was also responsible for keeping his side in the game at times during the first half, notably with a fine double save shortly before the half-hour mark.
City debutant Riyad Mahrez first drew a smart low stop with a free kick from just outside the area which squirmed out of Cech's grasp into a dangerous area, but the keeper reacted quickly to thwart Aymeric Laporte's follow-up effort from point-blank range.
Laporte had another opportunity from the resulting corner when he rose unmarked to meet Mahrez's delivery, only to glance his header comfortably wide of the target.
A difficult first half got even worse for the Gunners when Ainsley Maitland-Niles - already a makeshift left-back due to injuries to Sead Kolasinac and Nacho Monreal - was forced off, being replaced by Stephan Lichtsteiner for his debut in an unfamiliar position.
Mahrez came close again shortly before half time when he curled a trademark effort narrowly past the far post, but City were given a reminder of the precarious nature of a one-goal lead when Pierre-Emerick Aubameyang fired wide on the stroke of half time.
Arsenal were fortunate to go into the break only a goal behind, though, and City soon regained control of the game upon the restart with Aguero blasting one effort off target after the ball had fallen kindly for him.
Emery introduced Alexandre Lacazette in an attempt to change the course of the match, and the striker almost had an immediate impact when he collected the ball in space on the edge of the box, only to put his half-volley wide with the outside of his foot.
The chance seemed to inject some life into the hosts as City let their control over the game slip momentarily, although they should have restored it shortly after the hour mark when some suicidal defending left Aguero with a free run at goal from the halfway line.
The Argentine could have teed up the recently-introduced De Bruyne for a tap-in, but instead went for goal himself and was denied by a big save from Cech.
It felt as though it might be a pivotal moment in the match considering Arsenal's improvement leading up to it, but that did not prove to be the case and City did have their second goal just 50 seconds later when Bernardo slammed an unerring first-time finish into the top corner from Mendy's low cross.
The second goal effectively put paid to any hopes of an Arsenal comeback, although Mesut Ozil could have set up an exciting finale with two chances in the space of four minutes - first fluffing his lines from Lichtsteiner's cross and then failing to make the most of an Ederson error courtesy of a heavy first touch.
There was one final sight of goal for Lacazette in stoppage time too, but Arsenal could have few complaints at slumping to a defeat which proved that they still have plenty of work to do to banish the lingering ghosts of the Wenger era.
City, meanwhile, looked comfortable without being at their best, and now go into a run of games which sees them face all three of the newly-promoted clubs in the space of five matches. Arsenal, on the other hand, face an away trip to take on Chelsea at Stamford Bridge next.
ARSENAL (4-2-3-1): Cech; Bellerin, Mustafi, Sokratis, Maitland-Niles (Lichtsteiner 35'); Guendouzi, Xhaka (Torreira 70'), Ozil, Ramsey (Lacazette 54'), Mkhitaryan; Aubameyang
MAN CITY (4-2-3-1): Ederson; Walker, Stones, Laporte, Mendy; Gundogan, Fernandinho, Mahrez (De Bruyne 60'), Bernardo, Sterling (Sane 87'); Aguero (Jesus 79')