Liverpool put its miserable recent run behind it with a dominant performance to end Real Madrid's perfect Champions League start with a 1-0 win at Anfield on Tuesday.

Alexis Mac Allister headed in the only goal, but Madrid was grateful to goalkeeper Thibaut Courtois for keeping the score down.

Trent Alexander-Arnold was met with a hostile reception on his return to Liverpool, entering the game as a late substitute, and the home crowd roared the Reds over the line for what could be a turning point in their season.

Both sides are now tied on nine points from their opening four games of the league phase.

Liverpool had lost six of its previous eight games in all competitions, but stopped the rot by beating Aston Villa on Saturday, as Arne Slot resorted to a more tried and tested team selection.

Florian Wirtz replaced Cody Gakpo in the only change from the weekend, and Liverpool again looked more like the side that stormed to the Premier League title last season.

"It is easy to say now, because we won twice in a row," said Liverpool captain Virgil van Dijk. "In a world of chaos, you have to stay calm and take the right perspective.

"We all know how football works — it can change overnight."

Slot lauds defense

Mac Allister headed home the game's only goal in the second half of the well-earned win, as Slot's men handed the La Liga leader its first defeat this season in Europe's elite competition.

"Impressive, because we played against an incredible side, a team that's on an unbelievable run of form, only lost once, won all their other games," Slot said. "If you then can win against them and perform how we have, that's very positive," Slot said.

"It's been (some) tricky weeks for us, many away games, hardly any rest in between every single game. It helps if you can play in front of these fans and you can play in front of Real Madrid, because I think that brings out the best in my players and our fans.

"We had a very bad run of form in terms of results. No excuse in the world can make up for us losing so many games," Slot said.

"But, we had to play a lot of games in a small amount of time. Tonight, we played against a team that played on Saturday as well, so the both of us had two days' rest.

"And it's helpful to play in a home game, because, from the last eight, I think we played six away from home. So, the fans can give you just a little bit of an extra edge if you are maybe a little bit tired."

"A great performance ... It could have been a bit more maybe."

The Dutchman also praised his side's defensive discipline, especially in keeping Kylian Mbappe and Vinicius Junior quiet.

"I said before the game that they have scored 26 goals in La Liga, and Mbappe and Vinicius together have 24 goal contributions," Slot said. "So, if you want to win this game you have to make sure that these two are not on the scoresheet."

Slot singled out 22-year-old right-back Conor Bradley for his standout performance.