The German giants demonstrated their composure amidst a frenzied atmosphere in Glasgow.
Vincent Kompany, Bayern's manager, praised his team's maturity in dealing with the intense environment created by Celtic's 60,000-strong home support.
"It's cliche to say, but it's the first half of the game. Overall, it's a really great result," Kompany said after the match.
He acknowledged the challenge posed by the atmosphere, stating, "We dealt really well with the atmosphere for long spells before it could go too crazy."
The scoring was opened by Michael Olise, whose powerful shot from 15 yards found the roof of the net just before halftime.
England captain Harry Kane extended Bayern's lead early in the second half with a precise volley from a Joshua Kimmich corner.
Celtic, however, showed resilience, with Daizen Maeda pulling one back with a header in the 79th minute.
This late goal injected some hope into the home fans, but Bayern goalkeeper Manuel Neuer was crucial in ensuring the visitors maintained their lead, making a significant save from Alistair Johnston in the final moments.
Despite the defeat, Celtic's manager Brendan Rodgers remained optimistic. "At 2-1, Bayern Munich are hanging on. That's what we can take from it. We've got one more shot," Rodgers said.
He emphasized the learning curve for his players, stating, "It's a new level for a lot of the players, they've done absolutely great. Let's go and have no regrets and see where it takes us."
Bayern now look forward to a crucial Bundesliga match against Bayer Leverkusen this Saturday before hosting Celtic for the decisive second leg on February 18.
"We're also pretty decent at home so we'll look to play on that as well," Kompany added, focusing on the upcoming domestic challenge.
Celtic, on the other hand, will need to channel the spirit of their late surge if they aim to overturn the deficit and reach the Champions League's last 16 for the first time since the 2012-13 season.