Bojan Krkic gave Stoke the lead early on with a fine 20-yard volley, but was brought off with a worrying-looking knee injury after 30 minutes on Monday night, having gone down unchallenged inside the area.
Stoke doubled their lead after substitute Stephen Ireland tapped home from close range from Victor Moses’ low cross on 52 minutes, and Moses added a third with a fantastic curling strike from a tight angle.
Rhys Bennett pulled one back for Rochdale with 12 minutes remaining before Jonathan Walters added a fourth for Stoke in injury time, and Hughes’ Potters will travel to Blackburn in the fifth round.
The Premier League side killed the mood inside Spotland in the fourth minute through Bojan’s strike, volleying first time into the top left corner after the ball dropped to him on the edge of the area.
Stoke approached the game professionally for the first half hour and were well on top until Bojan was forced off injured, jarring his knee unchallenged inside the area and limping off to cause concern for Hughes.
At the other end, Rochdale grew into the contest, and Jack Butland had to be at his best to come out bravely and stop Stephen Dawson with the ball at his feet.
Rochdale had another golden opportunity just before half-time as Callum Camps played top scorer Matt Done through on goal, but he slid the ball a yard wide with Butland rushing out to block him.
Ireland, who came on for Bojan, turned home Moses’ fine cross after good work on the left for 2-0 to Stoke just after half-time, before Walters’ glancing header went just wide.
Moses added a third after more fine work on the left of midfield, advancing into the area and turning Joe Rafferty twice before producing a superb finish into the corner of the net.
Walters toe-poked an effort just wide of goal five minutes later as Stoke dominated, but Rochdale gave their fans something to cheer about through Bennett, finishing from eight yards after the ball dropped to him from a free-kick.
But Walters got the goal he had been craving in stoppage time, tapping home from Marko Arnautovic’s centre as Stoke counter-attacked.