Rodrigo scored twice to sink AZ Alkmaar as Benfica stepped up their pursuit of a first European trophy for over 50 years.
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Not since 1962, when 20-year-old Eusebio's second-half double clinched a 5-3 European Cup triumph over Real Madrid, for whom Ferenc Puskas scored a hat-trick, have Benfica got to grips with silverware against continental rivals.
It was the combination of Eduardo Salvio and Rodrigo that killed AZ. Salvio, the scorer of the only goal in the first leg, was the provider in Lisbon for both of Rodrigo's close-range strikes that secured a 2-0 win on the night for Benfica and 3-0 aggregate success.
The Portuguese giants, on the brink of earning their 33rd domestic league title, have looked as strong as any side in the Europa League, since being somewhat unfortunate to drop out of the Champions League.
PAOK, Tottenham and now AZ have been swatted aside, and Benfica are a side no other will fancy in the semi-finals.
Jorge Jesus has assembled during his five-year tenure a well-oiled machine, and with players of Rodrigo and Salvio's quality on the same wavelength it helps the coach's task.
Benfica suffered an early blow, however, when they lost right-back Silvio to an apparently nasty leg injury right at the start of the match, Andre Almeida taking over.
If AZ sensed that may help their cause, they were unable to capitalise.
Oscar Cardozo twice went close to opening the scoring, with Esteban making two strong saves, and Salvio also threatened before delivering the killer ball for the opening goal in the 39th minute.
Charging down the right, he produced the perfect low cross that skidded between defence and goalkeeper and into Rodrigo's path at the far post, where the striker slotted in.
Benfica, boasting a record that shows they had won nine of their last 11 European matches, drawing the other two, were two goals clear in the tie after their slender win in Holland.
Dick Advocaat's visitors needed to show purpose and adventure to regain a foothold but their display was largely flat.
The second goal of the night came in the 71st minute when Salvio, twice a Europa League winner with Atletico Madrid and runner-up with Benfica last season, dug out an even better delivery than his first.
From close to the corner flag on the right, he conjured a terrific ball that spliced the AZ defence again, leaving Esteban grasping at air as the cross reached Rodrigo again at the far post, where he volleyed in from five yards.
Argentinian winger Salvio might have had a third on the night, but it hardly mattered that this time Esteban defied Benfica with a blocking save.