The former Internazionale coach will have been more than satisfied as City overcame gritty opponents from the Potteries.
There was a wind of change as Mancini made five alterations to the starting line-up from the last match of Mark Hughes one week earlier.
While it was all smiles for Mancini, Stoke manager Tony Pulis was left to reflect on a fifth successive league match without a win which leaves them uncomfortably close to the relegation places.
City had two early shouts for penalties rejected in quick succession after appeals for handball against Abdoulaye Faye and a challenge by Andy Wilkinson on Robinho.
Stoke would have snatched the lead midway through the opening half but for a brilliant block by keeper Shay Given to deny Tuncay.
City's patience was finally rewarded when they made the breakthrough in the 28th minute when Carlos Tevez made a break before squaring the ball for Petrov to squeeze home at the far post.
It was Petrov's fourth Premier League goal of the season in only his fourth start of what was a largely dour opening period.
But in the third minute of stoppage time City unexpectedly doubled their advantage when Gareth Barry headed on a free-kick from Pablo Zabaleta and Tevez stuck out a leg to divert the loose ball past keeper Thomas Sorensen, his 10th goal of the campaign.
The home side came within a whisker of adding a third goal in the opening minute of the second half when Sorensen did well to deny Petrov and also Robinho as he was about to pounce on the rebound.
Pulis made all three substitutions in the opening 15 minutes of the second period to try to force their way back into the game.
And it so nearly worked as all three of the replacements almost scored as a Stoke goal would have reignited the drab second period.
James Beattie was denied by a super save from Given and from the resulting corner Robert Huth failed to hit the target with a free header, while not long afterwards Ricardo Fuller glanced a header narrowly wide.