Villa hat-trick inspires Valencia
The drama did not stop there as Benfica scored twice in the last 15 minutes to win 2-1 at Olympique Marseille and qualify for the quarter-finals while Anderlecht beat Hamburg SV 4-3, only to lose 6-5 on aggregate.
Liverpool, trailing 1-0 from the first leg, kept their campaign alive by beating Lille 3-0 at Anfield. Captain Steven Gerrard scored a ninth-minute penalty and Fernando Torres added two more in the second half.
Valencia, held 1-1 at home by Bremen, were 2-0 ahead in 15 minutes with goals by David Villa and Juan Mata.
Werder managed 27 shots on target but every time they got on the scoresheet Villa stopped the recovery in its tracks.
Hugo Almeida pulled one back for the Germans only for Villa to score again on the stroke of halftime.
Torsten Frings, with a penalty, and Marko Marin scored twice in five minutes to make it 3-3 with nearly half an hour still to play, but Villa put Valencia ahead again almost immediately.
The Spaniards held on for a 5-5 aggregate draw despite Peru forward Claudio Pizarro's late equaliser.
Benfica, held 1-1 at home by Olympique Marseille in the first leg, went behind to a Mamadou Niang volley in the 70th minute.
But the Portuguese side deservedly levelled four minutes later when Argentine Maxi Pereira exploited a blunder by the Marseille defence.
Brazilian Alan Kardec scored a last-gasp winner for Benfica leading to confusion in which the scorer was yellow-carded for a shirtless celebration and Marseille winger Hatem Ben Arfa, who had only just come on, was dismissed for kicking Javi Garcia.
Argentine forward Sergio Aguero scored twice in a four-goal first half as Atletico Madrid drew 2-2 at Sporting to progress on away goals after a scoreless first leg.
Anderlecht's 16-year-old forward Romelo Lukaku was among the scorers in Brussels where the home side, 3-1 down from the first leg in Hamburg, fell behind but hit back to lead 4-2 until their hopes were extinguished by Mladen Petric's 75th minute strike.
Standard Liege kept Belgian interest in the competition alive after a 1-0 victory over Panathinaikos with a Dieudonne Mbokani goal completed a 4-1 aggregate win over the Greek side.
Wolfsburg completed the evening's action by scoring in the last minute of extra time with a Christian Gentner goal to beat Rubin Kazan 2-1 and win 3-2 on aggregate.