Liverpool manager Arne Slot expressed relief after the Reds finally managed to beat Real Madrid for the first time in 15 years.
Second-half goals from Alexis Mac Allister and Cody Gakpo gave Liverpool a deserved win in a dominant performance against the Uefa Champions League holders whom they last beat in 2009.
Kylian Mbappe even missed a penalty as the holders suffered a third Champions League defeat in five matches.
However, Slot stressed he was not getting carried away by his team's perfect start that saw them return to the top of the table.
"You know how special it is to play against a team that has won the Champions League so many times. They were a pain for Liverpool for many years too," said Slot, whose team have now won five out of five in Europe's elite club competition.
"I think it’s always good to win a game, and especially a big game like this, because you face so many quality players," he added. "We are only five games in in the new format, we are happy where we are, but we’re not getting carried away."
Mohamed Salah also fired wide from the spot, but it mattered little as Liverpool secured a 17th win in Slot's first 19 games in charge.
Slot has already achieved what former boss Jurgen Klopp could not by defeating the Spanish giants.
Liverpool had a score to settle with Madrid, who were unbeaten in eight previous meetings between the sides, including Champions League finals against Klopp's men in 2018 and 2022.
With Liverpool dominating possession and chances, Mac Allister struck the opener in the 52nd minute after a neat one-two with Conor Bradley in front of a delirious Kop end at Anfield.
Gakpo sealed the game in the 76th minute with a header past Thibaut Courtois from an Andy Robertson cross.
The home side could have run away with the game in the first half, as Darwin Nunez had three glorious chances but found Courtois in formidable form. The biggest cheer of the first half came when right-back Bradley produced a stunning tackle to stop Mbappe's marauding run towards goal.
Caoimhin Kelleher's second-half penalty save against a confidence-sapped Mbappe brought one of the biggest roars of the night.
It marked another subdued and disappointing performance for Mbappe.
The Frenchman has had a challenging start to life at Real after joining from PSG in June, with just one goal in five Champions League games for the Spanish club.
The World Cup-winning forward has scored one goal in his last six games in all competitions but manager Carlo Ancelotti defended him as an "extraordinary" player who just needed support.
"It’s a difficult moment for him, we’ve got to support him and give him our love, he’ll soon be fine," Ancelotti said.
"It could be a lack of confidence maybe. Sometimes you have moments when things aren’t quite working out for you. But you get through these moments. People miss penalties, it happens a lot. You can’t put too much grief on him for that.
"He works hard, he’s got to keep working hard and fighting. You get through these moments. Things just aren’t running for him at the moment. We’ve got be patient. He’s an extraordinary player."
Dortmund on track
Borussia Dortmund eased past hosts Dinamo Zagreb 3-0 to stay firmly on course for a top-eight finish and automatic qualification to the knockout stage.
Jamie Bynoe-Gittens fired last year's finalists into a deserved lead in the 41st minute before the unmarked Ramy Bensebaini headed in their second goal in the 56th minute.
Forward Serhou Guirassy, back after a short illness, also got on the scoresheet in the 90th, slotting in after coming on as a substitute.
The Ruhr valley club, who also hit the woodwork twice, have now won four of their five matches in the competition despite struggling on the road in the Bundesliga this season with no away wins.
They are now on 12 points in fourth place of the new-format Champions League with three games left. Dinamo are on seven points in 23rd.
Meanwhile, Juventus drew for a second successive game in the Champions League with a 0-0 stalemate away to Aston Villa.
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 in a stalemate, 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.
