In the 15th minute, Mohamed Salah's right-footed shot from very close range to the bottom left corner was denied by a fine save from Real Madrid goalie Thibaut Courtois at Saint-Denis' Stade de France.
Five minutes later, Courtois made another amazing save, pushing Sadio Mane's stinging close-range drive onto the post.
Karim Benzema scored from the penalty area but it was disallowed by an offside call after a VAR (video assistant referee) check in the 44th minute.
The Reds dominated the first half of the final but neither team was able to break the deadlock despite both teams having chances at each end.
In the 59th minute, Vinicius Junior scored the winning goal for Real Madrid.
The kick-off was delayed for 36 minutes for security reasons, according to UEFA.
The Spanish football club added their 14th Champions League trophy to their collection -- five in the last eight years.
Real Madrid have won the title in 1956, 1957, 1958, 1959, 1960, 1966, 1998, 2000, 2002, 2014, 2016, 2017 and 2018.
Italian manager Carlo Ancelotti became the first to clinch four UCL titles.