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.
13. Jeremie Frimpong - 5
Came on in 82nd minute and stretched the Hearts defence on a couple of occasions with bursting runs without an end product Photo: Craig Foy - SNS Group
14. Diego Laxalt - 5
On for Taylor with eight minutes left of normal time but, other than providing fresh legs, made no real difference. Photo: Rob Casey - SNS Group
15. Mikey Johnston - 6
On for the start of extra-time and looked lively. Youngster was brave enough to take a penalty and converted with confidence. Photo: Craig Foy - SNS Group
16. Leigh Griffiths - 6
Typical impact after coming off the bench in the 97th minute. Put Celtic 3-2 up with poacher's finish and scored in the shoot-out. Standard Griffiths. Photo: Rob Casey - SNS Group