After falling 2-0 down on the night, substitute Marcos Llorente struck twice in extra-time and Alvaro Morata added a late third to ensure a famous victory for Diego Simeone's side against a Liverpool team unbeaten in their last 25 home games in European competition.
Bayern Munich, already crowned Bundesliga champions last week, lifted the league trophy in an empty stadium on Saturday after crushing hosts VfL Wolfsburg 4-0 on the final matchday. Bayern can win more silverware next week with the German Cup final against Bayer Leverkusen. They are also still in the Champions League.
Former Manchester United captain Roy Keane regrets having apologised to Alex Ferguson after the falling-out which led to him leaving the club in 2005, leaked extracts from his new autobiography have revealed.
A summary of Wednesday's matches in the UEFA Champions League.
Images from the Champions League matches played across Europe on Tuesday