Kick-off was delayed by 36 minutes due to chaotic scenes outside the Stade de France, which saw doors locked and fans gassed by French police.
The first half brought little mouth-watering action, and it all fell largely to Liverpool as their pressing play rocked the Spanish champions.
Mohamed Salah twice tested Real Madrid goalkeeper Thibaut Courtois in the first exchanges. Sadio Mane went even closer in the 21st minute with a low shot which Courtois managed to tip over 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 hold as the ball seemed to go out of Fabinho last, but former referee Peter Walton explained why it didn’t.
He told BT Sport: “It’s easy. Benzema is in an offside position. The offense is committed if the ball is deliberately returned to him.
“Fabinho, the ball deflects from him, he is not deliberately playing the ball to him. He is not playing with Benzema. It is only considered valid if the Liverpool player has deliberately played it. That is why he has it took so long for VAR.”
Rio Ferdinand added: “If I’m a Real Madrid player, I go crazy.”
Additional Reuters reporting.