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City's first half display was superb, with the movement and passing leaving Stoke chasing shadows.
The passing of David Silva, Kevin De Bruyne, Raheem Sterling and Sergio Aguero cut Stoke's defence to shreds at times and that it took 27 minutes for the Blues to break through was the only real surprise.
Sterling was first to go close as he cut inside and left four defenders in his wake before firing a curling shot inches over Shay Given's crossbar on 11 minutes. The hosts had to wait until the 14th minute for their first real attack - a resulting corner was headed clear by David Silva!
Then a flowing move between De Bruyne, Sergio Aguero and Silva created a chance for Sterling but his low shot lacked power and Given collected easily.
The Blues finally broke the deadlock on 27 minutes after Ryan Shawcross pulled Nicolas Otamendi back from a corner and referee Mike Dean awarded a penalty - emphatically dispatched by Aguero who banished memories of his double midweek miss in one fell swoop.
And the prolific Argentine doubled City's lead nine minutes later with a soaring glanced header from a De Bruyne free-kick - his 26th Premier League goal in his last 25 outings.
Willy Caballero preserved the Blues' two-goal lead with a fine stop from Phil Bardsley's far post volley just before the break and Diouf missed a sitter from six yards as the passage of play continued.
It was a reminder the hosts are no mugs and four minutes after the break, the Potters were awarded a penalty of their own as Sterling was adjudged to have impeded Shawcross from a corner. It looked soft, but Bojan scored to bring Stoke back into the contest.
With much of the second-half on a knife-edge as Stoke looked to find an equaliser and City's intricate play not quite as on the money as it had been in the first 45, but the Blues were never in any serious danger and four minutes from time, sub Kelechi Iheanacho broke through, rounded Given and picked out fellow sub Nolito who fired home to make it 3-1 and seal the points.
Deep into injury Nolito was given another gift he couldn't miss as Sterling raced clear before sliding in the Spaniard to tap into the empty net to complete a superb victory at a ground the Blues so often leave with little or nothing to shout about.
Immaculate defending from the young centre-half who oozes class. Dominant in the air and coolness personified on the floor, this was perhaps a glimpse of a future England skipper. His reading of the game and ability to pick out a pass make him a class act. Settling in well, you might say...
City overtake United on more goals scored at the top of the Premier League with today's victory. At a ground that the Blues had previously won just once at in eight attempts, this was an emphatic display and immediately answers the oft-asked question of whether Pep Guardiola's teams are capable of going to places like Stoke and playing the sort of football the Catalan demands.
Three wins from his first three games and nine goals on the road in two matches - nobody could ask for more.
City showed one change from the midweek win over Steaua in midweek with Nolito making way for Jesus Navas. Pablo Zabaleta was once given the armband.
City XI: Caballero, Zabaleta, Otamendi, Stones, Kolarov, Fernandinho, De Bruyne, Silva, Navas, Sterling, Aguero
Stoke XI: Given, Bardsley, Shawcross, Wollscheid, Pieters, Imbula, Whelan, Bojan, Allen, Arnautovic, Diouf
Kevin De Bruyne looks ahead to City's game against Schalke
The latest from Pep ahead of Wednesday's crucial Champions League tie against Schalke...