Aberdeen were also able to pick up three points away at Livingston and will anticipate a highly contested match as they try to reach their second Betfred Cup final in a row.
Hearts last-gasp victory over neighbours Hibs saw the Jambos register their first Premiership win of the season and since they beat Aberdeen in March at the end of the previous campaign.
The result has lifted the pressure on manager Craig Levein, who's disastrous start to the season has seen overwhelming numbers of supporters at Tynecastle start to actively call for his head.
Derek McInnes' Aberdeen were able to put last week's disappointing 1-1 draw with St Johnstone behind them in their 2-0 victory at Almondvale against Livingston on Saturday, although the result certainly flattered the away side.
Despite coming under some criticism himself, McInnes' side now sits third in the Premiership and are unbeaten in their last four games.
Former Scotland boss Levein is still yet to win a trophy in his lengthy career as a manager, whilst his opposite number McInnes guided Aberdeen to success in the Scottish League Cup five years ago.
Both dugouts will know the importance of securing another visit to Hampden, in order to challenge the Old Firm in the cup competitions this season.
Hearts will still be without key men Steven Naismith, Jamie Walker and John Souttar, but could welcome back Austrian midfielder Peter Haring, who has not featured for the Jambos since the Scottish Cup final defeat to Celtic in May.
Derek McInnes has no fresh injury concerns ahead of the match, but still only has youngsters Lewis Ferguson and Dean Campbell as his only fit central midfielders.
Top striker Sam Cosgrove came off the bench in Saturday's win at Livingston but is expected to start for the visitors.
What the managers have said
Despite Sunday's crucial win over Hibs, manager Levein is not getting carried away.
Speaking at his official pre-match press conference, he said: "We have got work to do. I'm not celebrating. I didn't celebrate on Sunday. I didn't think it was appropriate.
"We just need to get ourselves back in a good position before I can think of anything like that."
Derek McInnes spoke of his desire to taste further success in the cup competitions but also stressed how difficult a test he was anticipating.
Addressing the media at his own press conference, he said: “We have always seen the importance of cup football at the club.
“Hearts are a good team and it is that bit more difficult when you go away from home.
“I think that being on grass, it is a tight surface at Tynecastle but it is always a good surface, hopefully, that we can enjoy the game a bit more."
Kick-off at Tynecastle is at 7.45pm on Wednesday 25th September 2019 with highlights available after the match on Sportscene.