A sweet volley in the 30th minute by Ibrahim Afellay and substitute Phil Bardsley's low 75th-minute strike sealed the triumph at the Britannia Stadium that took the Potters into the League Cup last four for the first time since 1971-72, the season in which they won the trophy.
Wednesday had demonstrated their capacity to spring a shock in the previous two rounds with victories over Stoke's fellow Barclays Premier League sides Newcastle and Arsenal.
But the Sky Bet Championship outfit rarely looked like threatening an upset on this occasion, with the hosts in control more or less throughout.
And Hughes, whose only negative on the evening was the early loss of Peter Crouch to a hamstring injury, said afterwards: "I was pleased with the performance - we got the job done.
"Sheffield Wednesday are a good team, as they proved in previous rounds, and it was important not to underestimate the challenge.
"We went into it with the right mentality, understood what we needed to do well and it was quite a straightforward victory in the end - we didn't allow them to get any foothold in the game or momentum to their play.
"I'm really pleased with the amount of control and our ability to manage the game to a conclusion."
Stoke now face a two-legged semi-final against one of Manchester City, Everton and Southampton or Liverpool - with the latter pair playing each other on Wednesday night - and Hughes is feeling good about the Staffordshire club's chances.
"It's a big challenge for us because there are some very good teams still left in the competition and it will be difficult to overcome whoever we come up against," said Hughes, whose side beat holders Chelsea in round four.
"But I think we are enjoying these games and we'll look forward to the two huge ones in the coming weeks
Over two games I think we'd back ourselves against anybody.
"Southampton we beat a couple of weeks back, we did the double over Everton last season, we have beaten Manchester City and Liverpool, I seem to recall, we beat in the last game of last season, so we have got a chance."
Stoke, currently 12th in the Premier League, have achieved two consecutive ninth-placed finishes since Hughes took charge and this cup run shows his tenure continues to go from strength to strength.
"It's another step," the Welshman said.
"We want to have a good season league-wise, which we fully anticipate we will, but to add a good cup run...it's the first time we have got to a League Cup semi-final in 40-odd years, so it's been a long time, but now we're there it's a case of trying to get to the final.
"We'd love to do that and if we can get silverware, all well and good
We'd be delighted if we could."
Wednesday boss Carlos Carvalhal was keen to pay tribute to his players' efforts over the course of their entire cup run, as well as to the club's supporters, more than 4,500 of which were in attendance.
Carvalhal said: "I'm unhappy because we are out but I am happy about what we did in the whole competition.
"We put out two strong teams in Arsenal and Newcastle and I must congratulate my players - and our fans, who were amazing again
Our best player was the fans."
He added: "We played against a very strong team and Stoke deserved to win
They had more of the ball, even though I don't think our keeper had too much work to do."
Source : PA
Source: PA