Manuel Pellegrini’s team were fitful in attack, a far cry from the silken fluency demonstrated by Stoke as match-winner Arnautovic struck a post and passed up two further chances to claim the matchball.
The Premier League leaders could end the weekend in fourth place after a display that made a mockery of their lofty status.
They began the day by welcoming back goalkeeper Joe Hart, while David Silva made his first Premier League start since October 3 and Wilfried Bony deputised for the injured Sergio Aguero up front.
Geoff Cameron replaced Charlie Adam in central midfield for the hosts, but it was Hughes’ forward reshuffle that caught the eye and it paid handsome dividends after seven minutes.
Shaqiri was the architect, skipping around a sprawled Fernando and engineering space for a low cross that Arnautovic dispatched from close range.
Kevin De Bruyne shot too close to Jack Butland in the Stoke goal before his team were left with a mountain to climb – Fernando again made to pay for over-committing on Shaqiri, who threaded a delightful throughball for Arnautovic to clip beyond Hart.
Arnautovic was twice agonisingly close to completing a first-half hat-trick as Stoke’s quicksilver attacking play continued to cause the shambolic visiting defence countless problems.
First the Austria international flashed a header from Glenn Whelan’s cross wide of the near post with Hart beaten before Shaqiri sent him clear of City’s blundering backline to rattle the upright two minutes from the break.
It was a similar story upon the resumption – fleeting moments of encouragement for Manchester City’s attacking riches while Stoke appeared far more likely to contribute something of substance.
A firm hand from Hart prevented Bojan from adding a third having sashayed around Martin Demichelis with mocking ease and Arnautovic was unable to smuggle home the rebound.
Bojan’s next piece of sorcery was a beguiling backheel that released Arnautovic, who flashed the ball across the face of goal when seeking to return Shaqiri’s earlier favours, and Hart charged from his goal to deny the ex-Barcelona man once more before he departed to a rousing 71st-minute ovation.
Fernando’s nightmare showing was cut short by a hamstring injury as Manchester City limped to the finish line with 10 men, Aleksandar Kolarov rippling the side netting in a fleeting display of defiance.