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Olympiakos became the first Greek club to lift a European trophy.
Villa's inability to open up the defence was in stark contrast to El Kaabi, who only needed the slightest sniff of a chance against the English side to put the ball in the net.
Hummels headed home from a corner five minutes into the second half to send the Germans, who won the title in 1997, into their first final in Europe's top club competition since 2013.
Bayern, with only the Champions League title left to fight for, had scored twice in four minutes early in the second half through a Leroy Sane strike and Harry Kane penalty to turn the game around before Vinicius' spot kick.
Islamic State was alleged to have threatened four venues for this week's Champions League matches, including the Parc des Princes in Paris and two games in Madrid hosted by Real Madrid and Atletico Madrid.
Ten cities across Germany - Berlin, Cologne, Dortmund, Duesseldorf, Frankfurt, Gelsenkirchen, Hamburg, Leipzig, Munich and Stuttgart - will stage the matches.
Paris St Germain, who are seeking their first Champions League title, will take on Barcelona while Atletico Madrid face Bundesliga side Borussia Dortmund, which means all three Spanish teams have the opportunity to reach the semifinals.
Manchester United were one of the first to say they remain committed to playing in competitions run by Europe's soccer governing body UEFA, as did German champions Bayern Munich.
The EU's top court ruled that FIFA and UEFA abused their dominant position by forbidding clubs outright to compete in a ESL, but added that the competition may still not be approved.
On Monday evening at the end of a Super Lig match, Ankaragucu club president Faruk Koca entered the pitch and punched referee Halil Umut Meler in the face.