Liverpool are the only team with a perfect record in this season's Champions League after beating title-holders Real Madrid 2-0 in their heavyweight clash on Wednesday, with last season's runners-up Borussia Dortmund among the night's other winners.
The showdown at Anfield saw Real attempting to extend a run of eight games unbeaten against Liverpool.
However, Arne Slot's Premier League leaders were too strong, with Alexis MacAllister putting them ahead early in the second half.
Kylian Mbappe endured a frustrating night and squandered a chance to equalise for Madrid after an hour when his penalty was saved.
Mohamed Salah then missed from the spot at the other end but substitute Cody Gakpo headed in Liverpool's second goal on 76 minutes.
They are the sole side with five wins from five in this new-look Champions League, and are now guaranteed to advance at least to the knockout phase play-offs in February.
"You know how special it is to play against a club that won this Champions League so many times, are the reigning champions and were a pain in the ass for Liverpool many times as well," said Slot.
Real have lost three of their five matches and with six points they are currently 24th, the very last qualifying spot for the knockout phase.
Madrid coach Carlo Ancelotti had words of comfort for their star French striker, saying: "This is a difficult moment for Mbappe. We will support him and give him love."
Inter Milan sit second on 13 points, followed by Barcelona and Dortmund each on 12, with the Germans winning 3-0 against Dinamo Zagreb in Croatia.
A great goal by English youngster Jamie Gittens gave Dortmund a first-half lead, before Ramy Bensebaini headed in on 56 minutes and substitute Serhou Guirassy sealed the win late on.
VILLA, JUVENTUS DRAW
Aston Villa started with three straight victories in the Champions League but were six matches without a win in all competitions before hosting Juventus.
The game ended 0-0, with the English side denied in stoppage time when a Morgan Rogers goal was disallowed for a foul on goalkeeper Michele Di Gregorio.
Villa are just outside the top eight places offering direct access to the last 16, as one of seven teams on 10 points with three fixtures remaining.
Monaco missed the chance to cement their top-eight spot as they went down 3-2 at home to Benfica in a dramatic game.
Eliesse Ben Seghir gave Monaco an early lead but the visitors were level just after the break as Vangelis Pavlidis profited from a defensive error to score.
Monaco were reduced to 10 men when defender Wilfried Singo was sent off for a second yellow, but they still retook the lead as Soungoutou Magassa fired in.
However, Benfica's numerical superiority made the difference late on as Arthur Cabral headed in on 84 minutes and Zeki Amdouni snatched the winner.
Lille closed in on securing at least a play-off spot as they won 2-1 in Italy against Bologna, who remain winless.
Belgian-born midfielder Ngal'ayel Mukau was the French side's hero with a brace, including the opener before halftime.
Colombian defender Jhon Lucumi equalised for Bologna, but Mukau struck again on 66 minutes to secure Lille's third win in five matches.
PSV COMEBACK
Celtic and Club Brugge remain on course for the play-offs after drawing 1-1 in Glasgow, Daizen Maeda's superb strike earning the Scottish champions a point after they had fallen behind to a farcical Cameron Carter-Vickers own goal.
The comeback of the night came from PSV Eindhoven, with the Dutch champions recovering from 2-0 down to win 3-2 against Shakhtar Donetsk.
Goals by Danylo Sikan and Oleksandr Zubkov had the Ukrainians 2-0 ahead at halftime at the Philips Stadion.
However, they had Brazilian full-back Pedro Henrique sent off on 69 minutes and fell apart late on.
Malik Tillman's free-kick was carried over the line by the goalkeeper on 87 minutes and the same player equalised with a superb long-range strike in the 90th minute.
Tillman's fellow American Ricardo Pepi then got the winner in the fifth added minute.
Red Star Belgrade got their first points by coming from behind to hammer Stuttgart 5-1 in Serbia.
Ermedin Demirovic gave the Germans an early lead, but Silas Katompa Mvumpa, on loan from Stuttgart, equalised before goals by Rade Krunic and Mirko Ivanic, and a Nemanja Radonjic brace.
Austrian champions Sturm Graz are also off the mark after beating Girona 1-0 with a Mika Biereth goal.