The back-to-back shut outs in Helsinki and Helsingborgs represents the club's best record on the Continent for nine years.
The Hoops cemented their growing reputation with another frugal showing in the goalless draw against Benfica to open group G.
That was the fourth Euro game in succession they have not been breached, and the single goal scored by Helinski at Parkhead back on August 1 remains the only time that Fraser Forster has been beaten in five Champions League outings.
The man charged with organising the defence, assistant boss Johan Mjallby, believes they can hold out again tonight as they face Spartak in Moscow.
The no-nonsense Swede – himself a formidable star in the Celtic backline which went all the way to the Uefa Cup final in 2003 – is confident Forster and the players in front of him are learning quickly how to cope with the rigours of European football.
Mjallby said: "I can see signs that we have learned from the Europa League last year when we had a good run.
"It was a similar situation in that people were already counting us out and saying that we were just there for the taking.
"But we showed we can compete with teams that were nearly as good as Champions League teams.
"That's why we believe in ourselves. The good thing about this team is that we've shown we can get results away from home as well.
"That's why we are not too down about not winning our first game against Benfica.
"I wish we had three points in the bag already, but if you do not win games, then you have to make sure you don't lose them.
"We are still there in the mix. If we can defend the same way we did against Benfica, and improve a little bit going forward, they are beatable."
Mjallby wants more of the same tonight and said: "It was a very good team performance against Benfica. The players worked ever so hard for each other.
"They were spot on and did really, really well all over."
It is another step up again from being hard to beat to becoming a team who can win when faced with the cream of the Continent.
But Mjallby is backing this group to make that leap.
THE Swede said: "I always see myself as a winner in football, and I'm quite used to winning. I always believe in the team, and I know the manager does as well.
"Now they are up against the best teams in Europe, and we are delighted.
"The football is different, especially tactically. You have to have patience. You can't just go gung-ho and think you are going to score in every attack. Sometimes in the league we try to force things too much and go forward all the time.
"In Europe you have to be patient because a lot of the teams are very skilful, but they try to slow things down and then they just explode.
"You really need to be 100% focused all of the time because sometimes, when you think nothing is going to happen, they're at their best.
"So, this kind of football is definitely different, and the players have to prepare themselves for that.
"We do our homework and show the players what kind of opponents they are coming up against."
In pursuit of improvement, Mjallby, along with Celtic boss Neil Lennon and the rest of the backroom staff, have carefully analysed the testing 90-minute introduction their side got to Champions League group stage football against Benfica at Parkhead. The findings have been passed on to the players.
HOWEVER, Mjallby has acknowledged that one of the toughest things they must learn is how to cope with the pressure of simply being a Celtic player.
"We have a squad now and have to keep an eye on all the competitions we are in," said the Hoops No.2.
"When you play for Celtic, it is not acceptable to lose, in a way. The winning mentality is something we are trying to instil into the players.
"I think they are improving. For each of the seasons I have been here, the squad has improved on its mental strength.
"Most players now understand it is so important for us to win. And, if we can't do that, at least make sure you don't lose.
"We are improving every day when it comes to that. Now and then we will not be able to play fantastic football, and it is not always going to go our way.
"That is when you have to be mentally strong, take your chances and keep a clean sheet."
No one feels – or shows – the disappointment of the team not playing as well as they can more than Lennon.
But Mjallby reckons it is no bad thing that the man at the top wears his heart on his sleeve.
"We will always be a bit unhappy of we don't win, but it is good for the players to get that from the manager," he said.
"After a game there is nothing you can do about it.
"If you have made any mistakes and not had a good game, you have to make sure you are up for the next one and try to make sure you do not repeat that performance."