Last season's runners-up won 1-0 in Holland in the first leg a week ago and took a step closer to a repeat final appearance after again proving too strong for AZ.
Rodrigo, who had a loan spell at Bolton earlier in his career and has been linked with Arsenal, opened the scoring six minutes before half-time and then added a second inside the final 20 minutes.
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 won a European trophy.
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.
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 Eduardo 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.
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 72nd 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.