The champions kept up the pressure on neighbours Manchester United - 4-0 winners at Wigan - as they patiently broke down the visitors' stubborn defence to win thanks to goals from Pablo Zabaleta, Edin Dzeko and a Sergio Aguero penalty.
The only disappointment for manager Roberto Mancini was the loss of the Argentine striker with an apparent hamstring injury 15 minutes from the end.
Mancini's men were certainly good value for the three points with keeper Joe Hart a spectator for long periods. Stoke mustered a solitary shot in the first half as City tried to unpick the Premier League's meanest defence.
The home side had to wait until the 42nd minute before making the breakthrough. Zabaleta started and finished the move, combining with James Milner to beat Asmir Begovic from six yards after the Stoke keeper had saved the England midfielder's cross with his foot.
The hosts could have been ahead in the opening minute when Milner linked up with Aguero forcing Begovic into a smart save at his near post.
The Argentine came even closer on 33 minutes, hitting the upright with a flick header from Gareth Barry's cross.
Zabaleta's goal meant a change of tactics for Tony Pulis' men with the disappointing Kenwyne Jones taken off after just five minutes of the second half.
And the visitors' task was made even harder six minutes later when Dzeko made the most of a handling error by Begovic to tap in the home side's second. Aguero weaved his way into the Stoke box and stabbed a shot at the Stoke keeper who spilled the shot into the path of the Bosnian to tap in from two yards out.
The away side had a golden chance to make a swift reply but Jon Walters made a total hash of Cameron Jerome's neat flick to spoon his effort over the bar from just four yards out.
The game was made utterly safe on 74 minutes, Aguero scoring from the spot after Steven N'Zonzi clipped David Silva - although the initial challenge appeared to be just outside the box. The Argentine's penalty was close to Begovic but the Stoke keeper was unable to keep it out.
The spot-kick was Aguero's last act before he pulled up clutching his left hamstring to be replaced by countryman Carlos Tevez.
The home side looked like adding to their tally in the final stages although it was Stoke who came the closest, Joe Hart turning Glenn Whelan's drive onto his left-hand post to maintain a welcome clean sheet for the champions.