Toni Kroos struck the only goal as Real Madrid beat Galatasaray 1-0 in Istanbul to kick-start their Champions League campaign.
Real, who began the game bottom of Group A, clinched their first win in the tournament this season to ease the pressure on boss Zinedine Zidane - Jose Mourinho has been linked with his job.
Zidane's side were knocked off top spot in LaLiga by Barcelona after Saturday's 1-0 defeat at Mallorca but responded with a crucial win, which could have been by a wider margin had it not been for Galatasaray goalkeeper Fernando Muslera.
Muslera made a string of outstanding saves to keep Galatasaray in the tie, while the Turkish side were not without their chances.
Paris St Germain maintained their 100% record with a 5-0 win at Club Brugge, with Kylian Mbappe scoring a second-half hat-trick.
Mauro Icardi had given the visitors an early lead but it took until Mbappe's arrival as a substitute for PSG to take control of the contest.
Mbappe opened his account nine minutes after coming on and completed his hat-trick in the 79th and 83rd minutes after Icardi had grabbed his second of the night.
Robert Lewandowski has now scored 57 Champions League goals, only four players in the competition's history have scored more.— Squawka Football (@Squawka) October 22, 2019
Climbing the list of legends. 🙌 pic.twitter.com/K4zzg4pVW5
German champions Bayern Munich needed two goals from their top scorer Robert Lewandowski to sneak past hosts Olympiakos 3-2 and remain top of Group B.
The Greeks scored on the break when Kostas Tsimikas's cross found Youssef El Arabi at the far post and the Moroccan beat keeper Manuel Neuer.
Bayern, struggling for form since their 7-2 win at Tottenham Hotspur earlier this month, recovered to level with Lewandowski in the 34th minute.
He then put them ahead, stabbing in from close range against the run of play in the 62nd for his 18th goal in 12 games in all competitions.
Corentin Tolisso added a third with a curled shot in the 75th before the Greeks cut the deficit with Guilherme's deflected effort four minutes later.
Tottenham produced the ideal response to their Champions League humiliation against Bayern Munich with a 5-0 thrashing of Red Star Belgrade.
Erik Lamela and Son Heung-min were among four players to come into the starting XI after Saturday's draw with Watford and Lamela's ninth-minute corner was headed home by Harry Kane.
Lamela then set up Son to make it 2-0 after 16 minutes and Son grabbed his second of the night before Lamela made it 4-0 in the 57th minute, swivelling on the penalty spot to fire into the top corner.
Kane completed the rout with his second 18 minutes from time as Spurs moved up to second in the group behind Bayern.
Raheem Sterling scored an 11-minute hat-trick as Manchester City came from behind to beat Atalanta 5-1, although the evening was soured by an injury to Rodri and a red card for Phil Foden.
Atalanta took the lead from the penalty spot after 28 minutes after Fernandinho brought down Josip Ilicic and Ruslan Malinovskyi sent Ederson the wrong way from 12 yards.
However, City responded quickly and were back level within six minutes as Sterling clipped in a cross from the edge of the area and Sergio Aguero calmly tapped home on the volley.
Aguero made it 2-1 from the penalty spot after Sterling had been brought down by Andrea Masiello and the England international grabbed his first of the night on 58 minutes from Foden's pass.
Sterling made it 4-1 six minutes later after picking up Ilkay Gundogan's through ball and he completed his hat-trick after 69 minutes from Riyad Mahrez's cross.
In the other game in Group C, Shakhtar Donetsk came from 2-1 down at home to Dinamo Zagreb to draw 2-2, substitute Dodo equalising within 10 minutes of coming off the bench.
Juventus looked in danger of losing their unbeaten record this season when they trailed to Aleksey Miranchuk's 30th-minute goal at home to Lokomotiv Moscow, but Paulo Dybala struck twice in the space of three minutes to secure a 2-1 win.
Juventus and Atletico Madrid are tied on seven points in Group D after Alvaro Morata's 78th-minute header gave the Spanish side a 1-0 win over Bayer Leverkusen.