The Championship side knocked out Aberdeen, Dundee United and St Johnstone on their way to the League Cup final against Ross County at Hampden Park on March 13.
Hibs also disposed of Edinburgh rivals Hearts in the last-16 of the Scottish Cup after a replay, although the Easter Road side have come down from the high of that derby win by losing their last three league games to trail leaders Rangers by 14 points.
However, Stubbs, who confirmed defender Paul Hanlon will be out for four weeks with a thigh injury - the defender was suspended for Sunday anyway along with Marvin Bartley and Jason Cummings, is looking to get back on track against the cup holders.
He said: “The players have responded against Premiership opposition every time they have come up against them this season and on Sunday we are looking at another opportunity to perform and progress into the next round.
“Their manager John Hughes is an ex-team mate of mine and his teams always fight so we are expecting nothing less from their team.
“They will go into the game thinking that they can get a result.
“It has probably been quite a while since the holders retained the cup and they will have aspirations of doing that and we have aspirations of stopping them.”
The former Everton and Celtic defender insists confidence has not been dented with three successive defeats for the first time this season, to Morton, Dumbarton and Queen of the South.
He said: “We have had a disappointing week in terms of results, not in terms of performances.
“It is the first time I have had to say that all season.
“We have to take a step back from everything. It has dented our aspirations to go up automatically but otherwise, it has not stopped us from achieving what we want to do.
“It hasn’t had an effect on confidence. I could easily have been standing here talking about what a great week we have had with three wins, that’s how close the games have been.
“This is another competition that we are doing well in and it is a chance for us to progress into the semi-final.
“That’s the way we are looking at it.”
Hanlon hobbled off during last weekend’s defeat at Dumbarton but Stubbs revealed the fear of a more damaging knee injury for the 26-year-old was unfounded.
He said: “It is bad news and good news. At one point we thought it could have been his knee and a lot more serious and we are glad to say he has just got a rupture of his thigh, which is potentially going to keep him out for the best part of four weeks.
“When you look at that, compared to six to nine months when it could have been his knee, then it is really good news.”
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