It may not have been a vintage performance from Neil Lennon’s side, who were twice pegged back by their Championship opposition, but it was nonetheless a historic achievement for the Parkhead club, and a momentous moment for Scottish football.
Here’s how the Celtic players rated:
Player ratings scale - 10: One of the best performances you have seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
5. Greg Taylor - 6
A mixed bag. Had some good moments in the first half but like the team his performance dipped in the second half and was replaced by Laxalt. Photo: Craig Foy - SNS Group
6. Callum McGregor - 6
Cruised the first half and provided bursts of energy but was also posted missing for large spells as Hearts took control after the break. Photo: Alan Harvey - SNS Group
7. Scott Brown - 7
Involved in plenty of the action. Never rose to the bait from Naismith or Halliday as he dictated the first half. Looked to be struggling with the pace after the break but his desire for Celtic's third showed why he was included. Photo: Alan Harvey - SNS Group
8. Ryan Christie - 6
Scored a stunning opener but struggled to find that spark for the rest of the 120 minutes and was too often guilty of giving away possession. Saw his penalty saved in the shoot-out. Photo: Rob Casey - SNS Group