The brilliant Brazilian produced another super showcase of his extraordinary skills and a master class in finishing as he was the difference between the two teams, hardly surprising bearing in mind he cost a British record £32million.
The treble took Robinho's total to six goals since his move from Real Madrid and he could easily have scored a further three goals for City, who ended a run of three Premier League games without victory in style.
While Robinho won the plaudits, goalkeeper Joe Hart also deserved recognition with a string of fine saves on the day it was announced he had signed a new five-year contract.
Robinho might have given City a third-minute lead but for a brilliant tip over form keeper Steve Simonsen.
And it was inevitable that Robinho should make the eventual breakthrough in the 14th minute. Shaun Wright-Phillips crossed from the right with Elano and Ched Evans helping the ball on to Robinho, who fired home from ten yards.
Stoke were unfazed by the setback and had three great chances to get back on level terms.
Ricardo Fuller was denied by a superb stop from Hart who also did well to keep out a close-range header from Ryan Shawcross.
And in the dying seconds of the half, Fuller missed another clear-cut chance, blazing over from 18 yards when he ought to have hit the target.
City were forced to make a substitution just before the break when Evans, who was replacing the unwell Brazilian Jo, limped off with a knee injury to be replaced by Daniel Sturridge.
And it was Sturridge who set up Robinho's second goal soon after the restart. He made a terrific run, cutting in from the right, before releasing Robinho with an inch-perfect pass and the Brazilian could not miss from eight yards with a well-placed shot.
Robinho was denied a hat-trick twice in the space of a couple of minutes by super saves from Sorensen, as each time he looked set to find the net.
Robinho was finally rewarded for his considerable efforts with the third goal after a neat build-up which ended with Sturridge squaring the ball into the path of the Brazilian, who scored with a sweet finish.
Stoke, in fairness, kept battling to the end with Salif Diao and substitute Dave Kitson having chances to at least have got the Potteries side on to the scoresheet.