Stephen Ireland marked his first start for the club with the opening goal and Peter Crouch, on his return to the side, struck with the last kick of the game to secure a 2-0 win at Prenton Park.
The Potters, who made seven changes for the tie, will now travel to Birmingham in the next round.
Hughes said: "I was really pleased with how we went about our business tonight.
"When you have a fixture like this in the early rounds of the cup, if you don't approach it in the right manner and give respect to the opposition, and make sure your work is correct, you can cause yourself problems.
"But from the first minute I could tell the lads were focused on what was required.
"There was a good tempo to our passing and our play. We played some really good stuff at times.
"We were in total control of the game, which was really pleasing."
Ireland is hoping to rejuvenate his career under his former Manchester City manager Hughes after joining on a season-long loan from Aston Villa.
The Irishman was at the heart of much of Stoke's good attacking play in the first half, in which they squandered numerous opportunities to make the win more comfortable, before being removed after an hour.
Source: PA
Source: PA