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.
1. Conor Hazard - 6
The 'keeper had some nervy moments during the 120 minutes, and was culpable for Hearts' third goal, but redeemed himself with two penalty saves in the shoot-out. Photo: Craig Foy - SNS Group
2. Kris Ajer - 6
Not as effective at right-back as he has been of late. Rarely seen as an attacking outlet after the first half, and reverted to centre-back for extra-time. Held his nerve to score the winner in the shoot-out. Photo: Craig Williamson - SNS Group
3. Shane Duffy - 5
Positionally all over the place - often caught too deep or too high. Replaced by Mikey Johnston at the end of 90 minutes. Photo: Rob Casey - SNS Group
4. Christopher Jullien - 5
Involved in a couple of mix-ups and generally wasn't commanding enough when Hearts applied pressure. Photo: Alan Harvey - SNS Group