No one felt the embarrassment of Madrid's 2-0 loss at Anfield more than Kylian Mbappe, the superstar added in the off-season by the storied club that also were European champions against Liverpool in the finals of 2022 and 2018.
Mbappe had a penalty saved in the second half and was earlier dumped on his behind by Conor Bradley's perfect tackle.
Liverpool's Conor Bradley (right) tackles Real Madrid's Kylian Mbappe at Anfield. (AP PHOTO)
Monaco missed a chance to go second in the table, giving up a lead playing with 10 men from the 58th minute in a 3-2 loss at home to Benfica. Swiss forward Zeki Amdouni scored the winning goal in the 88th minute.
Borussia Dortmund, beaten finalists against Madrid in May, are up to fourth place after beating Dinamo Zagreb 3-0.
Champions League standout Jamie Gittens now has four goals in five games, curling a rising shot in the 41st minute to open the scoring.
The best comeback was at PSV Eindhoven, where the home team trailed Shakhtar Donetsk by two goals in the 87th minute, before a 3-2 win was sealed by US forward Ricardo Pepi's goal deep in stoppage time.
US defender Cameron Carter-Vickers scored an embarrassing own goal for Celtic - playing a no-look pass far beyond goalkeeper Kasper Schmeichel - in a 1-1 draw with Club Brugge.
Liverpool's stand-in right back Bradley was a standout on Wednesday (Thursday AEDT), playing a key pass that set up Alexis Mac Allister to score the opening goal in the 52nd minute.
After Mbappe's penalty was pushed away by goalkeeper CaoimhÃn Kelleher in the 61st minute, Liverpool star Mo Salah missed with his spot-kick in the 70th, before substitute Cody Gakpo sealed the win with a header in the 77th.
Madrid have now lost three of five games after defeats at Lille and at home to AC Milan. The record 15-time European champions have another tough trip next, at fifth-placed Atalanta on December 10.
Congo teammates Ngal'Ayel Mukau and Silas impressed in wins for Lille and Red Star Belgrade.
Mukau scored twice in 12th-place Lille's 2-1 win at Bologna, and Silas levelled for Red Star in a 5-1 rout of Stuttgart, though he barely celebrated his goal. Silas is on loan with the Serbian champions from Stuttgart.
In England, Aston Villa drew 0-0 with Juventus.
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