Harry Kane was on target as Bayern Munich beat Celtic 2-1 in Glasgow in the first leg of their Champions League play-off on Wednesday, 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.
“I know this place, I know it transcends performance sometimes. We dealt really well with the atmosphere for long spells before it could go too crazy.
“The last 10 minutes we had to defend and we did that well. Of course, you can feel in those moments, if the game comes alive it is a special place.
“The fans haven't seen many losses here, especially in Europe, so we appreciate the importance of the game and the victory.”
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.
Monaco had Libyan midfielder Moatasem Al-Musrati sent off in the 52nd minute, when the recent signing from Besiktas gestured to the referee calling for a yellow card after his teammate Breel Embolo had been fouled, only to be handed a second caution himself.
Benfica will hope to finish off the tie in next week's return, with the winners facing either Liverpool or Barcelona in the last 16.
In Rotterdam, Feyenoord shook off the sacking of coach Brian Priske on Monday to beat seven-time European champions AC Milan 1-0 and gain the upper hand to take to San Siro for the return.
The Dutch side were helped by a clanger from Milan goalkeeper Mike Maignan, who allowed Igor Paixao's speculative third-minute shot to ricochet off his body and into the net.
That was the only goal of a match played in driving rain at De Kuip.
“These evenings are why we do this,” said Feyenoord captain Quinten Timber.
“De Kuip was on it again. We were on it. On to next week,” he added, with Inter Milan or Arsenal awaiting the winner in the next round.
Earlier, Club Brugge beat last season's Europa League winners Atalanta 2-1 in Belgium thanks to a controversial stoppage-time penalty.
Ferran Jutgla gave the Belgian side a 15th-minute lead as Atalanta were punished for sloppy play at the back, but Mario Pasalic headed in an equaliser for the visitors before the break.
That looked to be that until the hosts were awarded a penalty at the death when substitute Gustaf Nilsson went down after being caught in the face by the outstretched arm of Atalanta defender Isak Hien.
The contact appeared to be accidental and not serious, but the referee stuck by his decision after reviewing the images, and Swedish forward Nilsson swept in the penalty.
“I've only just seen the footage and I reckon that if you ask 100 people if that was a penalty all 100 would say no. It's very strange,” complained Atalanta's Charles De Ketelaere.
Whoever wins that tie will face Aston Villa or Lille next.
