Reuters reports bidding to win back-to-back Champions League titles and a record extending 15th European crown, a disciplined Real seemed content to sit back against a tame Liverpool who carried little threat for most of the game.
They ensured victory with just over ten minutes to go when Karim Benzema scored the winner.
Meanwhile Napoli are through to the quarter finals for the first time.
Forward Victor Osimhen struck either side of halftime to steer the Italians to a comfortable 3-0 victory over Eintracht Frankfurt.
The result gave the Italian club a 5-nil aggregate win.
Prior to the game fighting broke out in the Italian city as fans set a police car on fire and threw stones at buses and police.
Italian authorities had banned German fans from attending the game amid concerns about possible violence, but some Eintracht supporters made the trip to Italy anyway.
Real Madrid's Karim Benzema. Photo: Photosport