They took the lead through Sergio Aguero's penalty, and he doubled their advantage 10 minutes later with a fine headed finish.
Stoke pulled a goal back through Bojan's spot-kick, which seemed to be a debatable decision from Mike Dean, only for Nolito to kill the game off late on.
City strike twice in 10 minutes to take comfortable lead
The game was quite tight and tense in the opening 15 minutes, with Aguero's attempt at providing Raheem Sterling with a simple tackle scuppered by an overhit cross. Stoke, on the other hand, were having very little joy coming forward; Giannelli Imbula and Marco Arnautovic both failed to provide the necessary cross when they finally got free.
After the teams had settled, it began to liven up. Both Ryan Shawcross and Joe Allen were required to make desperate sliding tackles to prevent Aguero and Sterling from getting shots off on goal, before racing straight up the other end. The ball fell kindly for Imbula on the edge of the box, but he scuffed his shot and City were able to clear.
Just as Stoke looked to be building up a head of steam, disaster struck. Shawcross hauled Nicolas Otamendi to the ground inside the area from a corner, and Mike Dean was left with little option other than to award a spot-kick. Despite missing from 12 yards twice during City's midweek trip to Romania, he confidently sent this one into the top corner.
Shay Given saved superbly with her feet moments later from the tricky striker, whose shot almost crept between his legs at the near post. There was little he could do about Aguero's second, though, as Guardiola's men doubled their lead less than 10 minutes after opening the scoring; Kevin de Bruyne's inch-perfect cross was glanced home.
Stoke's penalty heartache, then luck but second half fails to spark
That was not the final major moment before the break and Stoke could count themselves very unlucky to not have a penalty of their own. After Phil Bardsley's effort was well-saved by Willy Caballero, Allen attempted to turn in the box but was instead bundled over by Aleksandar Kolarov. Mame Biram Diouf headed well wide from a cross back in.
The second half brought no changes at the break, though it did see Stoke start much better and they were suitably rewarded. How their goal came about was slightly dubious, as Dean decided a light hand on Shawcross' chest from Sterling was enough to award a penalty. Bojan wasn't too bothered, in a carbon copy of Aguero's spot-kick.
Oddly, though, Stoke were unable to kick-on and ramp up the pressure. Instead, aside from Arnautovic failing to strike Allen's cross first time, the two teams were largely locked in a midfield battle that had no easy route out. Stoke brought on Jonathan Walters with 20 minutes to go but he failed to have the desired impact.
The Potters were then killed off by a late third from City, as a classy counter proved too much for Stoke's defence to handle. After winning the ball back, Kelechi Iheancho exchanged passes with several team-mates to work his way through the middle and then round Given. The chance looked to be gone, until he squared for Nolito to tap in his first goal in his new colours. A similar break in the final minute of added time saw Sterling unselfishly square to the Spaniard to cap off a superb win.
City now join their Manchester neighbours at the top of the table, which could be a familar sight this season. Stoke have just a point from their first two games, but can take heart from a spirited showing in the second half.