Alexis Mac Allister scored the only goal of the game at Anfield with a 61st minute header.
The result left both Real Madrid and Liverpool on nine points from their opening four games, in fifth and sixth place respectively, on the league standings.
Real shotstopper Thibaut Courtois had to be at his best to deny Dominik Szoboszlai, Virgil van Dijk, Hugo Ekitike and Florian Wirtz, who all had good chances, but he could do nothing to keep out Mac Allister's powerful header from Szoboszlai's cross.
Liverpool head coach Arne Slot hailed his side's performance against an "incredible" Real Madrid.
He said after the game: "Impressive because we played against an incredible side that is in an unbelievable run of form, only lost once, won all the other games.
"If you can win against them but also put in the performance we had that is very positive."
Slot's side came into this game on the back of six defeats in seven matches, having last overcome Aston Villa 2-0 at the weekend.
"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, but we had to play a lot of games in a small amount of time," added the Reds boss.
Real boss Xabi Alonso, meanwhile, admitted his side wasn't at the best in front of goal. He said: "I think we competed well. We played with a good rhythm.
"What we lacked was to hurt them in the final third. It was just small details.
"We conceded lots of fouls, Thibaut Courtois wasn’t able to save that header from a set-piece and it was difficult for us today but I am not going to complain about my team, we gave it a good go.
“We need to view this as an isolated defeat. We competed well; we were equal to them. We’ll learn from it.”
