Stephen Ireland marked his first Stoke start with a goal as the Potters claimed a place in the fourth round of the Capital One Cup.
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Former England striker Peter Crouch added a last-gasp second as Mark Hughes' side saw off League One Tranmere 2-0 at Prenton Park.
Irish midfielder Ireland, hoping to rejuvenate his career after moving on a season-long loan from Aston Villa, struck midway through the first half with Crouch striking with the last kick of the game.
Stoke should have won more comfortably and spurned numerous other chances, particularly in the first half.
They were almost made to pay as Jean-Louis Akpa Akpro and Chris Atkinson went close for Rovers in the second half but the Merseysiders were to rue the misses as Crouch had the final say.
Stoke had made seven changes, which included giving Ireland a run from the kick-off after two substitute appearances and a first start of the season for Crouch.
Hughes also rested first-choice goalkeeper Asmir Begovic to give Thomas Sorensen 90 minutes while Jermaine Pennant and Wilson Palacios were other inclusions.
Tranmere, having won just once and lying 19th in League One, were not expected to provide much opposition and even rested their veteran 40-year-old defender Ian Goodison with other matters pressing.
The Premier League side's superiority, despite the changes, was evident from the outset and, as appears to be becoming customary under Hughes, they passed the ball around effortlessly.