Harry Kane was on target as Bayern Munich beat Celtic 2-1 in Glasgow in the first leg of their Champions League play-off, while there were also wins for Benfica, Feyenoord and Club Brugge.
Bayern are hoping to go all the way to this season's final, which will be played at their own Allianz Arena in Munich on May 31.
They threatened to run riot against the Scottish champions at Celtic Park as they dominated the first half and took the lead just before the interval thanks to a superb Michael Olise strike.
Bayern's second goal came just four minutes after half-time, with the unmarked Kane scoring with a cushioned finish at the back post following a corner.
It was Kane's seventh goal in this season's Champions League, and his 29th in 29 games in all competitions.
However, the Bundesliga leaders took their foot off the pedal after that, allowing Celtic – who had a first-minute Nicolas Kuehn goal disallowed for offside – to come back into the game.
Brendan Rodgers' team pulled one back as Daizen Maeda scored following a corner with 11 minutes left, but they could not find an equaliser.
"It's cliche to say, but it's the first half of the game. Overall, it's a really great result," said Bayern coach Vincent Kompany, according to the BBC.
Celtic's first home defeat since December 2023 leaves them facing a huge task to try to turn the tie around in Germany next Tuesday, with the winners going through to face either Bayer Leverkusen or Atletico Madrid in the last 16.
"It's only a one goal difference. It's a big challenge, we know that but it's still a possibility," insisted Rodgers.
Elsewhere, Vangelis Pavlidis scored the only goal as Benfica won 1-0 away to Monaco, as the home side were forced to play much of the second half with 10 men.
Benfica had won 3-2 in Monaco in the league phase in November and they came out on top again at the Stade Louis II thanks to a Pavlidis strike just after half-time.
It was the Greek international's sixth goal in his team's last five Champions League outings, a run which includes a hat-trick in the dramatic 5-4 loss to Barcelona last month. (AFP)