AC Milan in the Champions League are a much more potent force than Hearts in the SPFL Premiership.
But for Neil Lennon's side, it is an intoxicating blend which they are now proving they can handle without appearing punch drunk.
The manner of the 3-1 win at Tynecastle - with goals from Kris Commons, Anthony Stokes and debut Bhoy Teemu Pukki - confirmed the Hoops were not prepared to be distracted by the prospect of their opening Group H game in the San Siro on Wednesday.
Lennon had demanded they retained their full focus, even threatening to rethink his selection plans for midweek if anyone gave anything less than their all at Tynecastle, either mentally or physically.
His words clearly resonated with his players, and they can now board their flight to Milan tomorrow morning with momentum and confidence.
"We would have lost that game last year, so, they have changed their mentality, which is great," is Lennon's succinct assessment of how his squad has developed over the past 12 months.
He insists that, despite wide-held belief to the contrary, Celtic do not have the biggest of squads, especially when they are being challenged to fight on two fronts.
So, Lennon will continue to field his strongest side - or as near as possible - in every game.
By the end of the group stage, when injuries and fatigue will be sure to take their toll, he will almost certainly be forced to modify this approach.
But, for now, in what is still the fledgling stage of the campaign - even though they have already played 11 games - Lennon wants to build up as big a head of steam as he can.
Ensuring they do not lose any more ground to Inverness in the title race - they are three points behind having played a game less - is an important part of the psychological battle to be won.
And the group which heads to Milan will carry with them a feel-good factor, knowing they performed in a dominant fashion to eliminate any threat Hearts may have presented to their San Siro prep.
Lennon said: "I am not saying we are going to go to Milan and be blaze about it. We are not. But we will not be fazed by it."
Lennon headed to Turin from Tynecastle to watch Milan draw 2-2 with Torino, a result which left the Hoops' Serie A opponents with concerns over more dropped points, their form and another couple of injuries.
By contrast, the Celtic hope to have James Forrest fit to return after missing Saturday with a recurrence of his sciatic nerve problem.
And Lennon reckons Adam Matthews - forced off after damaging his left ankle against Hearts - will also be fit to fight for a place in their starting XI.
The manager reported: "It looked like a jolt, a twisted ankle.
"But the physio is saying he's hopeful he'll be okay for Wednesday."
The Welshman linked up very well with Mikael Lustig playing behind, and their delivery into the opposition box was a feature of the game.
The commanding presence of Scott Brown - has he ever played better on such a consistent basis? - was another key plank in this win.
The enthusiasm and energy of the young Hearts side had to be matched, then stifled, and Celtic did this with assurance, even after Jason Holt had cancelled out the first-half lead the Hoops had taken when Commons scored from the spot after Willie Column harshly adjudged Jamie Hamill to have deliberately used a hand to block a Stokes volley.
"We looked powerful, as you'd expect against a young team," reflected Lennon. "But we were very professional.
"Our reaction to the Hearts goal was excellent, and with just a little more care with the final ball and finish, we'd have won more comprehensively."
Stokes can be exonerated from any such criticism, given how important a role he played in all three goals.
The Republic of Ireland striker forced the award for the first, scored the second with a very cool and clinical finish after sub Georgios Samaras and Commons had used their heads to put him through, then saved the very best for last.
A 70-yard run from his own half took Stokes to the byeline, where, having seen his first effort blocked, he had the cool thinking and ability to lift the ball over the defenders and keeper on to the head of Pukki - just on for Commons - who nodded in from close range.
Stokes has now scored four league goals this season, and has underlined his claims for a rare Champions League starting place on Wednesday.
Lennon said: "He took his goal brilliantly, but his overall play is getting better and it was a wonderful bit of skill for the third. I don't know how he did it, and I'm sure Teemu was delighted to see that."
As were all the Celtic fans occupying the stand behind the Hearts goal who got a close up view of a man on top form.
It's just a pity that, once again, they were not prepared to let Stokes and Co. provide the fireworks on the day.
Just days after it was revealed Uefa had fined the club €5000 for pyrotechnics being let off during the home match against Cliftonville, another flare and banger were discharged.
Celtic must now wait to see if the SFA or SPFL will investigate the incident, and hope there is no repeat of these idiotic actions in the San Siro.