Despite dominating for long periods, the Dutch succumbed to a sweet strike from the Argentine just after the break
Jorge Jesus' men have reached the semi-final and the final of the competition in their last two attempts and look on course to go one better this term after a hard-fought away win in Netherlands on Thursday.
While they showed little of the attacking threat that saw them score nine goals in four Europa League games before their trip to the AFAS Stadion, they ground out a victory that puts them in the driving seat in the tie.
Benfica rarely threatened before the break but were able to keep an occasionally lively AZ front line at bay before taking their golden opportunity soon after the interval.
Two minutes into the second half, Benfica had their lead, as Eduardo Salvio opened his account for the season with a vital away goal.
After Oscar Cardozo's effort was well saved by Esteban Alvarado, the loose ball fell to Salvio, who produced an excellent finish to edge the visitors in front.
It leaves AZ with an uphill task to progress, given that Benfica have won 10 of their last 11 games at the Estadio da Luz - keeping clean sheets in all those victories.
In a low-key start, AZ had the better of the opening exchanges with Roy Beerens having en effort saved by Artur Moraes before curling a shot from the left-hand side wide of the far post.
While the visitors grew into the game, Aron Johannsson was next to threaten as he drew a smart save from Artur following positive play again from Beerens, with the Benfica goalkeeper required again to beat away Steven Berghuis' strike soon after.
For Benfica, it was a case of lacking a final ball, as they failed to create anything for wily striker Cardozo.
Things were made more difficult for the visitors when Ruben Amorim was taken off injured, although they would have gone ahead at the break had Guilherme Siqueira and Rodrigo not blazed efforts over the crossbar from inside the area.
After a first half with few efforts on target, Benfica needed just three minutes of the second to take the lead, as Salvio pounced on Cardozo's saved effort to angle an effort home.
It killed any momentum that AZ may have had and Jesus' men will be more than happy to take their slender advantage back to Lisbon, especially given that AZ have not won on the road in any competition since mid-February.