The Parkhead side beat Swedish outfit Elfsborg 1-0 at home in the third qualifying round first leg on Wednesday night.
The Scottish champions were not at their best, but did enough to take a slender advantage to Scandinavia next week. A Kris Commons header on 76 minutes broke the deadlock, and allowed the home faithful a sigh of relief.
A clean sheet in the home leg will be vitally important for the Hoops, as they travel to Boras for the return fixture next week.
Celtic boss Neil Lennon was pleased with his side’s performance, despite admitting that they were not at their best.
"I am delighted with the performance and the result. They made it difficult for us to break them down but it was not frustrating, it was understandable.
"We weren't at our best but that was always going to be the case, there is still a bit of rust there. We still have a lot to do in the tie but we are confident.
"The crucial thing is clean sheet. That is important. If we score over there Elfsborg have got to have three. The tie is probably in the balance but we are confident that we can go there and get a result.
"The Astroturf might change things with the way I pick my team. But I was pleased with result. I would have taken 1-0 before the game."
Celtic fans will be concerned that their side lacks firepower after the sale of star striker Gary Hooper to Norwich, and Anthony Stokes started the game furthest forward for the hosts.
Much of the attention was on Mo Bangura, who played for the visitors against his parent club, and was treated to boos from the Celtic Park faithful.
Lennon had tried to prevent the 24-year-old, who is on a season-long loan at the Scandinavian club, from featuring in the fixture, to no avail.
Elfsborg manager Jorgen Lennartsson said that although Celtic were good value for their win, the tie was not yet over.
"They were the better side and deserved to win the game. But I don't think Celtic should feel that the tie is over because it is not. It was a very good first half and we played exactly the way we wanted.
"In the second half we were too deep and did not have enough possession, didn't create any chances – maybe one – and they pressed us hard. We hoped we could defend to get a draw but we conceded one goal.
"It was not good but we think the game is still alive. We have lost one of the last 25 game at home on our Astroturf. So it will be a different game, we have to attack, we will have the crowd on out side."
In other Champions League third round qualifiers there were no major shocks around Europe, with previous competitors in the tournament recording positive results.
The first legs saw wins for PSV Eindhoven, Lyon, Viktoria Plzen, FC Basel, Zenit St Petersburg and Metalist Kharkiv. Fenerbahce drew 1-1 in Switzerland against Salzburg.
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