The fixture rounded off a remarkable cup weekend, which saw the likes of Chelsea and Manchester City crash out to lower-league opposition, but Stoke rarely looked like missing out on progression.
Bojan Krkic opened the scoring with a stunning fourth-minute volley, before Stephen Ireland and Victor Moses added their names to the scoresheet in the second half.
Rhys Bennett netted a consolation for the home side with 12 minutes to go at Spotland, but Jonathan Walters made it 4-1 in stoppage time.
"We got the job done but credit to Rochdale," Hughes is quoted as saying by BBC Sport. "In the first half we found it difficult.
"We had a great goal from Bojan which helped us and, in the second half, we got to grips with them and turned it around.
"At the weekend a lot of teams fell by the wayside and we weren't going to let that happen to us.
"We wanted to make headlines for the right reasons and thankfully Rochdale haven't made the news."
One sour note for Hughes was a knee injury to goalscorer Bojan, who left the ground on crutches after being forced off on the half-hour mark.
Quizzed on the problem, Hughes added: "It is too early to know, he's going for a scan and hopefully it will be good news.
"Since he came to the club he has done things like that [the volley that opened the scoring], we see it in training every day."
Stoke will visit Blackburn Rovers in the fifth round.
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