The home side looked to be in control but keeper Joe Hart needed to produce two good saves to prevent Stoke equalising.
First, the England international dived to his left to tip away a shot from Ricardo Fuller, who was presented with the ball by City defender Tal Ben-Haim's miscontrol.
Then Hart, who signed a new five-year contract on Sunday, did well to keep out Ryan Shawcross' header from Tom Soares' right-wing corner.
Evans' injury was a blow for City but the Welshman's replacement, Sturridge, produced a moment of brilliance to set up Robinho's second goal just after the break.
Pulis frustrated by lack of luck
Sturridge ran at the heart of the Stoke defence before threading through a perfect pass for his team-mate, who made no mistake.
City's Micah Richards blazed over from eight yards before yet another run from Robinho ended with a curling shot which Sorensen did well to save.
And Sorensen came up with an even better stop when he blocked Robinho's shot at point-blank range after Wright-Phillips pulled the ball back from the right-hand touchline.
But Sorensen was helpless when another fine City move ended with the excellent Sturridge steering the ball across to Robinho, who calmly completed his hat-trick.
It was a miserable afternoon for Stoke, who remain in the bottom three and have now won just once in seven games.
They did put up a fight and Salif Diao's drive was tipped over by Hart before Dave Kitson missed their best chance of the second half.
Kitson, on as a substitute after being left out of the starting line-up, saw his header from Rory Delap's cross well saved by Hart.
Stephen Ireland should have netted a fourth for City in injury time but lifted the ball over the bar after being put through on goal by Robinho.
Manchester City boss Mark Hughes: "I thought we were excellent, and not only in the attacking sense because defensively we were rock solid. We were prepared to stand up to the battle that Stoke will always give you.
"When we got the ball back we broke with real purpose and could have won by an even bigger margin.
"We need to win consistently and if we play like that, then it's possible. We need to be solid defensively, which we were, and the way we play we will always create chances."
Stoke manager Tony Pulis: "We were desperately disappointed to go in at half-time 1-0 down. I thought we created really good opportunities.
"We could have scored three or four goals and what killed us was their second goal just after half-time, which caught us cold.
"We need to be more resilient defensively, because we did cause problems going forward. We're disappointed to get nothing from a game we contributed a lot to."
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