England international Milner, on the day he turned 29, grabbed a last-minute winner after sparing City's blushes against the Championship side with a 66th-minute equaliser at the Etihad Stadium.
Milner's double came after he was pushed up front following a poor first half in which City fell behind to an Adthe Nuhiu strike in the 14th minute.
City boss Manuel Pellegrini suggested his team were complacent after a draw against Burnley last week and, after thrashing Wednesday 7-0 in September, the same issue may have resurfaced.
Their first-half performance was sluggish and lacked bite, although they fielded a strong side and began as if the fixture would pose few problems.
They controlled possession in the opening minutes as Bacary Sagna almost found space to shoot in the box and Jesus Navas blasted an effort well over.
But just as it seemed only a matter of time until the hosts took charge, they were caught on the break as Wednesday took a shock lead after 14 minutes.
The Owls had seen little of the ball but they made maximum use of it as Stevie May burst down the right and got behind the defence
May looked up and picked out Nuhiu with a simple pull-back to the edge of the area and the Austrian clinically side-footed past Willy Caballero.
The goal knocked City out of their stride and they struggled to muster a significant response
Simple passes started to go astray and a tetchiness became evident in their play.
Yaya Toure might have changed things as he strode through only to shoot wide and Frank Lampard missed the target when well-placed.
City also felt some rought treatment as Stevan Jovetic was updended crudely by May and referee Michael Oliver simply signalled play on.
Frustration continued as Lampard threaded Jovetic through only for the offside flag to be raised, and such was City's lack of cohesion that Toure was compared unfavourably to cult hero Carlton Palmer by Wednesday fans.
Pellegrini recognised something needed to change and switched shape for the second half with midfielder Milner moving into a more advanced role.
There was an immediate step up in tempo with Navas firing across goal and Toure having an effort blocked but it was not until David Silva and Samir Nasri entered the fray that City got back into the game.
The two playmakers were introduced just after the hour and their introductions paid instant dividends as Nasri cut inside from the left to pick out Silva and his flick put Milner through
Milner showed good composure to steady himself and drive home an equaliser across Chris Kirkland.
The relief was evident but City still struggled to create the chances to kill the game.
Toure curled a shot narrowly wide but Wednesday were resolute and frustrated the hosts in possession, with Jose Semedo a notable thorn in their side.
The Owls also had some moments of their own as Claude Dielna and Jacques Maghoma got in shots but Caballero was not seriously threatened.
Silva might have settled the contest in the last minute but Kirkland met his shot with a fine save.
Wednesday might have thought they were there but the relief was only temporary
As the game went into four minutes of injury time Silva again picked out Milner and he finished calmly from close range.
Source : PA