STORY: Vinicius Junior scored just before the hour with Real's first attempt on goal and their goalkeeper Thibaut Courtois made several fine saves to deny Liverpool, who end the season with two domestic cups having also failed to win the Premier League.
In a battle of European heavyweights, Juergen Klopp's side had more opportunities but lacked sharpness when it mattered as Carlo Ancelotti became the first coach to enjoy double Champions League success with two clubs having triumphed with AC Milan.
It was LaLiga title holders Real's fourth Champions League crown in seven years as they improved their impressive record in the competition with their eighth victory in as many finals.
"It was so emotional. I cried and scream because I am a Real supporter to the core. My blood is white, not red. I love Madrid with my entire soul and I am super happy," said Real Madrid supporter Antonina Cadena as she left the Bernabeu with thousands of other satisfied fans.