They still have two chances of being at Hampden, too.
Just a week after a victory over Spartak Moscow secured their place in the last 16 of the Champions League, Neil Lennon's side moved into the fifth round of the William Hill Scottish Cup at Gayfield last night.
There was no Parkhead roar or stirring theme music to inspire the Hoops this time out, however.
The glory here was found only in the winning, with Adam Matthews' first-half strike enough to see off a plucky Arbroath and ensure that the dreams of a potential domestic clean sweep are still alive this morning.
Their progression should have been secured long before the final whistle blew, with a plethora of chances passed up at Parkhead in the first meeting and again on a chilly night on the east coast.
This had all the hallmarks of a potential banana skin as Lennon's men faced an in-form Arbroath impressing in the Irn-Bru Second Division and full of confidence after their Glasgow heroics.
The upset never materialised, however, with Celtic able to head home with their place in the next round, and a trip to Raith Rovers, tucked away in their back pockets.
It was little surprise that the Celtic boss made wholesale changes to the side that failed to complete the job the first time round, with just three – Efe Ambrose, Matthews and Scott Brown – retaining their place from the original tie.
It was a signal of Lennon's intent and perhaps a warning to his faltering stars that if they fail to impress when given the chance they may have to wait some time for another opportunity to make an impression.
The Hoops started with purpose and determination, no doubt eager to put the game beyond their Second Division hosts as quickly as possible.
But despite taking the lead through Matthews, Arbroath grew into the encounter as time elapsed, nervousness creeping into Celtic's play as their part-time foes sensed another remarkable result
That followed a first half that saw the SPL champions narrowly miss putting their hosts to the sword as they pressed for goals.
Just 10 minutes in they thought they had given themselves the perfect start as Lassad Nouioui converted at the back post, but his effort was ruled out for offside.
That denied the Hoops a well-worked goal after Brown had sent Georgios Samaras clear with a lovely touch on the edge of the area.
On the half hour mark, the unfamiliar pairing of Nouioui and Samaras ought to have produced a goal, but as the Greek diverted a long ball into the path of his fellow forward, Lassad could only contrive to pass up the chance at the back post.
It was a good job, then, that Lennon's side were already a goal to the good, with the Hoops' profligacy giving the hosts plenty of reasons to believe as they tried valiantly to venture upfield and relieve some pressure.
Matthews was the man Celtic had to thank for giving them the lead, the defender bagging his first goal in green and white, and only the second of his career, in some style as he nipped in to pinch the ball off Colin Hamilton's toe on the halfway line before striding forward and firing a terrific effort into the top corner.
At the other end, Fraser Forster and his defensive line were hardly under siege but there was still the odd moment of anxiety for the Hoops, with lone striker Steven Doris a hard working and impressive figure for the Red Lichties.
Clear scoring chances were sparse, but Celtic would have been well aware of the dangers of penalty box pinball as Arbroath launched crosses into the area, eager to launch themselves into aerial challenges and hustle and bustle their opponents at every opportunity.
Paul Sheerin's men thought they had pulled themselves level as Forster spilled a cross and Doris converted in the second half, but referee Craig Charleston spared the Englishman's blushes, blowing for a foul on the keeper. It appeared to be a soft call, but it proved crucial for Celtic.
With little over 10 minutes remaining, there was another huge let-off, with Forster this time the hero as he sprinted from his line to deny the onrushing Connor Birse.
The forward was only on the field a matter of seconds but he saw his shot blocked by the keeper's legs causing it to spin agonisingly wide of the far post.
It was job done for Celtic on what was a tough night for the Hoops.
Wembley remains something to dream about. Hampden, however, remains a far more realistic prospect.