Mac Allister heads Liverpool to Champions League win over Real Madrid

Liverpool's Alexis Mac Allister headed a second-half winner as the hosts earned a hard-fought 1-0 victory over Real Madrid in a battle between European giants on Tuesday, handing the LaLiga leaders their first defeat in the Champions League this season.

Arne Slot's men climbed to sixth in the table with nine points after four games of the league stage, one place below Real who are level on points but lead on goal difference.

Liverpool, who three days earlier halted a dreadful four-game Premier League losing streak, battled from the start and kept Real goalkeeper Thibaut Courtois on his toes before Mac Allister finally broke the deadlock in the 61st minute.

Dominik Szoboszlai, who was outstanding all night, sent in a beautiful free kick and the Argentine rose the highest to head home and send Anfield into raptures.

Liverpool briefly celebrated what they thought was a penalty in the first half when Szoboszlai blasted the ball off the arm of Aurelien Tchouameni, but the referee decided there had been no handball after a VAR review.

"I think it was a good game against a really good team," Mac Allister said. "(Courtois) is a fantastic keeper - we all know. He had a few saves, so again I think he's a really good keeper but today I think we were better and deserved to win."

Szoboszlai had several terrific chances on the night. Courtois stopped what might have been a simple tap-in off Florian Wirtz's cross when he threw up a leg to stop Szoboszlai's shot in the first half. The Hungarian forced a couple more diving saves from Courtois before halftime.Real's best chance before the break was Jude Bellingham's shot from a tight angle that lunging Liverpool keeper Giorgi Mamardashvili got a foot on.

Kylian Mbappe squandered a great chance for Real in the second half when he fired wide of the far post.

COURTOIS RESCUES REAL AGAIN

Liverpool looked sure to go 2-0 up in the dying minutes when Mohamed Salah found Cody Gakpo in front of goal but Courtois made another brilliant save and Salah's follow-up was blocked.

"I think there was a lot of energy and a lot of hard work," Van Dijk said. "Obviously, (Real) have won 14 in the last 15 - they have a lot of quality. We know their strength. So, we had to be spot on in everything we do. I think we performed our game plan perfectly.

"It is easy to say now because we won twice in a row - in a world of chaos you have to stay calm and see perspective of things."

Courtois called the loss "a shame."

"I tried my best to keep the team in the game, but in the second half we committed too many fouls near the box and they're good at that," Courtois told Spanish broadcaster Movistar Plus.

"It's always hard playing here. We have to earn it and play better. A match like this is decided by small details."

Long-time Liverpool player Trent Alexander-Arnold, who departed for Real in the close season, was a late substitute and was booed mercilessly whenever he touched the ball. Hours earlier, a commemorative mural of Alexander-Arnold, who played 354 games for Liverpool and won seven major trophies, was vandalised.

"It was an intense game, top top class in European football," Real boss Xabi Alonso said. "We needed (Alexander-Arnold's) quality, we needed his threat from the wing, (the boos) could be expected, he is professional and was ready for it."