The Edinburgh clubs lock horns in Sunday’s fifth round tie at Tynecastle, a year after Hibs, who went on to lift the trophy after a 114-year drought, won a replay between the sides at the same stage.
Hibs are six points clear at the league summit and have made it clear that gaining promotion back to the Premiership is their priority following a three-season absence.
Former captain and manager Stanton believes progress in the cup can enhance their objective of taking the chequered flag in the second tier.
He said: “It means a lot to Hibs just to keep their season going. It keeps the confidence high for all the league games that will be coming up between now and the end of the season. The wee spell that Hibs have had recently hasn’t helped matters.
“Every team goes through that type of thing. I would rather Hibs tripped up now as there would still be time to recover league-wise. They have to keep the momentum going in the league.
“Before you know it we will be looking at the end of the season and we know what we want to happen.
“We want Hibs to be out of this league and in the Premiership. I was about to say Sunday’s game is a side-event, but it’s not.
“If you are in the cup then you are in there to win it. If Hibs could win the Championship and retain the Scottish Cup I would be absolutely delighted.
“We are in them so why not try and win them?”
Hibs striker Jason Cummings, who has notched 15 goals this season, is set to return to the starting line-up at Tynecastle after being dropped for the weekend’s disappointing draw with Ayr United, but former defender Stanton insists there is too much of a burden on the 21-year-old to score.
He added: “You have to score goals to win games and Hibs can’t keep relying on Cummings to produce the goods.
“Other players have to take part and weigh in.
“The opposition players are looking for Cummings and marking him tighter because of his goalscoring reputation.
“It is up to others in the team then to assume that responsibility.
“People tend to forget his age at times.”
l Pat Stanton was speaking in his role as an ambassador for Business Fives, a nationwide 5-a-side football tournament.