Michy Batshuayi scored a dramatic winner for Chelsea as they came from behind to beat Atletico Madrid 2-1 in their new Wanda Metropolitano.
Despite an impressive performance against the Spanish giants, Antonio Conte's side looked like they would have to settle for a point on Wednesday night.
Antoine Griezmann opened the scoring for the home side, firing home a penalty from a foul from David Luiz. Alvaro Morata set up a grandstand finish with a fine second-half header to level the scores. But it looked like neither side would find a winner until Batshuayi turned in Marcos Alonso's cross right at the death.
Paris Saint-Germain proved too strong for Bayern Munich with a 3-0 Champions League victory at the Parc des Princes.
PSG headed into the game under a cloud after Edinson Cavani and Neymar had clashed over a penalty last weekend, but the French giants showed no signs of dressing-room discord as Dani Alves gave them an early lead.
Neymar bamboozled Bayern's defence moments after kick-off with a mazy run in from the left flank, and teed up Brazilian compatriot Alves to thrash home the opener after just 84 seconds.
Carlo Ancelotti's Bayern - who have endured a tough start this season - were unable to deal with Kylian Mbappe's pace either, and the French star was on hand to help PSG add their second.
Mbappe dribbled into the Bayern box and laid the ball off to Cavani, who found the back of the net with a rising finish that Bayern goalkeeper Sven Ulreich - in for the injured Manuel Neuer - could perhaps have done better to keep out.
Mbappe was again the instigator for PSG's third goal as he rolled David Alaba with a sensational turn before his cross-shot deflected into Neymar's path for a simple finish just past the hour mark.
In Portugal, Barcelona needed an own goal to overcome Sporting Lisbon while Juventus recorded their first three points of the Champions League thanks to 2-0 win over Olympiacos.
Romelu Lukaku was in inspired form as Manchester United clobbered CSKA Moscow 4-1 and Basel also recorded a big 5-0 win against Benfica.
Celtic stunned Anderlecht 3-0 and Roma beat Qarabag 2-1.
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