The Welshman scored one of the tournament’s finest-ever final goals to help end the Reds’ hopes of bringing the trophy back to Merseyside.
Liverpool were rocked 30 minutes into the tie in the Ukrainian capital Kiev as their talisman Mo Salah left the field in tears with a shoulder injury.
The Reds had nine shots with Salah on the pitch and none for the rest of the half.
Real Madrid scored their opener at 51 minutes after a gaffe from Reds keeper Loris Karius allowed Karim Benzema to score.
Liverpool’s only goal came when winger Sadio Mane netted four minutes later to equalise.
Bale had only been on the pitch two minutes before he rose in the air to execute a stunning bicycle overhead kick that found the top corner.
His goal put Real Madrid 2-1 up after 64 minutes.
Karius suffered further humiliation when Bale’s 83rd minute long-range strike slipped through his hands to deny Liverpool their sixth European cup.
Real Madrid’s victory in Kiev marks the third season in a row they have secured European club football’s biggest prize.
The Spanish giants have sealed their 13th European Cup, their fourth in five seasons.
Liverpool manager Jurgen Klopp’s long wait for a European trophy continues, after the German lost in the 2013 final as manager of Borussia Dortmund.
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The Reds’ leading scorer Mo Salah landed awkwardly after a collision with Real defender Sergio Ramos, causing him to leave the pitch with a suspected dislocated shoulder.
Ramos was jeered throughout the match after what was a devastating blow for the Liverpool fans.