Real Madrid have now won the Champions League for a record-extending 15th time, following their 2-0 win over Borussia Dortmund on Saturday.
The Spanish giants were out of sorts in the first half and struggled to keep pace with the Bundesliga side.
The German side hit a post and created two more clear chances in the first half as they threatened a big upset.
But Real have a unique relationship with this competition and, with an improved display after the interval, they finally came to life.
Toni Kroos – in his final game for the club – set up the opener with a corner for Carvajal to head home with 16 minutes to play.
Then Jude Bellingham rolled in Vinicius Jr to punish a stretched Dortmund side soon after.
