Hannover 96 1-2 Club Atlético de Madrid (agg: 2-4)
Mame Diouf's strike set up a tense finale but audacious goals either side of it from Adrián López and Falcao took the 2010 winners through.
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Club Atlético de Madrid booked their place in the last four of the UEFA Europa League with a second 2-1 victory against Hannover 96.
Los Colchoneros absorbed considerable pressure either side of the break but settled any nerves through Adrián López's classy second-half opener. Mame Diouf pulled one back for Hannover to set up an exciting finish, but an emphatic late strike from Falcao ensured it is Atlético who progress to face Valencia CF, whom they beat en route to winning the competition in 2010, in the semis.
A largely uneventful start suggested a tactical battle was in the offing, but with the onus on them to score Hannover eventually began to seize the initiative. Diouf provided a lively presence in attack as the hosts enjoyed plenty of possession in opposition territory, but Atlético defended well and chances remained scarce.
Hannover coach Mirko Slomka had suggested prior to the match that it was not in Atlético's repertoire to sit back, yet his prediction proved misplaced. Indeed, a solitary Adrián header which sailed comfortably wide was all the visitors had to show for the first half, but still it was they who maintained the aggregate advantage.
An even more courageous approach was required if Hannover were going to upset the odds and the risks involved served to open up the contest. With forwards of Atlético's quality, a single opening was likely to be enough and Adrián duly pounced on 63 minutes, turning Emanuel Pogatetz and dancing past goalkeeper Ron-Robert Zieler and Christian Pander to slot into an almost unguarded net.
Pander nearly caught out visiting keeper Thibaut Courtois with an audacious effort direct from a corner as the hosts desperately sought a route back into the tie, and Diouf gave them hope with a firm finish into the near corner with nine minutes remaining.
Yet Hannover's impeccable home record this season was ultimately spoiled by Falcao's thumping late winner, cushioning Diego's adroit chip and allowing it to bounce before applying an emphatic finish beyond Zieler. Diego Simeone's side will go into the last four with hopes high, even if they will be without the suspended Diego Godín for the first leg after a booking tonight.