Sergio Ramos' first-half goal was cancelled out by Yannick Carrasco in the 79th minute and the game went into extra time. Both teams failed to win in the added 30 minutes and the match went into penalties.
Juanfran saw his spot kick come off the post, before Cristiano Ronaldo tucked away his, to ensure the Santiago Bernabeu club won their second Champions League title in three years and their fifth since 1998.
Madrid manager Zinedine Zidane, who replaced Rafa Benitez in January, has also joined the exclusive band of men, who have won the holy grail as both player and manager.