Hearts took an early lead when the teams duked out an entertaining league game at Parkhead on Wednesday night but Celtic underlined their domestic supremacy and rallied to prevail 3-1.
Match preview
Robbie Neilson was rightly thrilled with the performance his side produced in the hardest fixture Scottish football has to offer as Hearts stuck to the game plan of trying to play through Celtic's famed and feared press.
Josh Ginnelly's opener was a perfect example of the bravery and fluidity Hearts played with; 12 seconds and four passes after Cammy Devlin won the ball inside his own half, Ginnelly was wheeling away in celebration after nodding in Andy Halliday's inviting cross.
Hearts could not maintain the blistering tempo playing at a raucous Celtic Park demands and Devlin was himself caught in possession when the hosts took the lead after the interval.
The Jambos have won six of their last seven home games, the only blemish being a 3-0 reverse when Rangers rocked up to the capital in February.
Celtic only narrowly emerged with all three points on their most recent visit to Tynecastle, with the lead swapping hands three times before the reigning champions ultimately earned a 4-3 win - Hearts are the only Scottish team to score as many as three goals in the same game against Celtic this season.
For the second outing in a row, Celtic conceded the opening goal in the sixth minute as Ange Postecoglou's 100th match in charge of the club threatened to become a landmark not worth remembering.
However, Kyogo Furuhashi emerged as Celtic's saviour once again, teeing up Daizen Maeda's first-half equaliser before finding the net himself on the hour mark - Sead Haksabanovic sealed all three points with a rasping drive into the top corner in the closing stages.
Celtic have now won their last 12 matches across all competitions and are yet to taste defeat since Real Madrid dismantled Postecoglou's side at the Santiago Bernabeu in November.
Boasting a nine-point lead at the Premiership summit, Celtic have already snagged the League Cup in their bid for a domestic treble while Hearts are trying to avenge the defeat they suffered against Rangers in last season's Scottish Cup final.
Celtic scored five goals against both second-tier Greenock Morton and top-flight St Mirren en route to this stage of the competition while Hearts followed up the satisfaction of an Edinburgh derby victory over Hibernian in the fourth round with a 2-0 win against Championship side Hamilton Academical.
Hearts Scottish Cup form:
W
W
Hearts form (all competitions):
L
W
W
L
W
L
Celtic Scottish Cup form:
W
W
Celtic form (all competitions):
W
W
W
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W
Team News
Neilson admitted that he was forced into most of the changes that he made for the midweek fixture, notably leaving out top scorer Lawrence Shankland from the entire squad.
The Hearts boss revealed that Shankland is "touch and go" for the cup tie but the absent duo Robert Snodgrass and Alex Cochrane "will be fine".
Ginnelly was forced off 38 minutes after nodding in the opener on Wednesday with complaints of muscle tightness but Neilson was quick to quash any fears of a lengthy absence and confirmed that the striker would be "fine" by Saturday.
This recent spurt of fitness struggles only adds to a lengthy injury list for Hearts which includes long-term absentees Craig Gordon (broken leg) and Craig Halkett (knee).
The duo of Beni Baningime and Liam Boyce are recovering from cruciate ligament injuries while Gary Mackay-Steven is struggling with a foot problem but, mercifully, Peter Haring has returned to training after a concussion absence.
Celtic's Maeda collided with Gordon's stand-in goalkeeper Zander Clark while scoring on Wednesday, sustaining a knee injury which is not season-defining but may sideline him for the cup clash.
James Forrest joined the scarcely spotted James McCarthy in the treatment room at Parkhead with a muscular issue but both first-choice full-backs Greg Taylor and Alistair Johnston are expected to return after they were rested for the midweek league game.
Hearts possible starting lineup:
Clark; Rowles, Sibbick, Hill; Atkinson, Devlin, Grant, Snodgrass, Cochrane; Ginnelly, McKay
Celtic possible starting lineup:
Hart; Johnston, Carter-Vickers, Starfelt, Taylor; Hatate, McGregor, Mooy; Jota, Furuhashi, Haksabanovic
We say: Hearts 2-3 Celtic
Hearts gave Celtic a scare in midweek and could be even stronger in front of their home crowd with some of their regulars back in the team.