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Benfica, who started the game with an aggregate lead of 3-1 thanks to a confident display at White Hart Lane a week ago, started brightly and weren't far away from an early goal when Luisao headed over the crossbar.
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Spurs created a great opportunity to pull a goal back midway through the first half when a cross landed at the feet of Roberto Soldado, but the Spaniard could only miscue his effort over the crossbar.
The visitors had looked relaxed in possession for the majority of the first half until a 34th-minute goal handed an even bigger advantage to Benfica.
Eduardo Salvio found it easy to skip past a couple of challenges on the right before chipping a cross into the box to find Ezequiel Garay, who powered a header past a helpless Brad Friedel to make it 4-1 on aggregate.
Benfica continued to ask questions in the early stages of the second half, with Salvio causing regular problems with his direct running at the visiting defence.
As time started to run out for Tim Sherwood's side, they managed to set up a dramatic finish to the tie with two goals in as many minutes.
Nacer Chadli pulled one back by using the space offered to him on the edge box to drill a powerful effort into the bottom corner.
Needing two more goals to force extra time, Spurs made it 2-1 on the night moments later as Harry Kane's header found Chadli, who turned to fire home from close range.
Tottenham dominated the closing stages of the tie and saw a penalty appeal rejected when Kane went down under a challenge in the box.
Spurs created one more clear chance in stoppage time when a cross reached Gylfi Sigurdsson, but the midfielder's effort was pushed past the post by Oblak.