Kick-off was delayed by 36 minutes due to chaotic scenes outside the Stade de France, which saw gates locked and fans tear-gassed by French police.
The first half brought little goalmouth action, and any largely fell to Liverpool as their high-pressing game rattled the Spanish champions.
Mohamed Salah twice tested Real Madrid goalkeeper Thibaut Courtois in the opening exchanges. Sadio Mane came even closer in the 21st minute with a low shot that Courtois managed to tip onto the post.
Real thought they had scored just before the break but striker Karim Benzema's effort was ruled offside after a lengthy VAR review.
The goal looked likely to stand as the ball appeared to come off Fabinho last, but former referee Peter Walton explained why it did not.
— Football on BT Sport (@btsportfootball) May 28, 2022
He said on BT Sport: “It is easy. Benzema is in an offside position. The offence is committed if the ball is deliberately played back to him.
“Fabinho, the ball deflects off him, he doesn’t deliberately play the ball to him. He doesn’t play Benzema onside. It’s only deemed onside if the Liverpool player has deliberately played it. That's why it took so long for VAR."
Rio Ferdinand added: "If I'm a Real Madrid player, I'm going bananas."
Additional reporting by Reuters.