The Portuguese side, who knocked out Tottenham Hotspur in the last round, gained a quarter-final, first-leg advantage thanks to Eduardo Salvio's goal four minutes after half-time.
Jorge Jesus' men will be confident of completing the job on home soil as Benfica try to reach the final for the second year in a row after losing to Chelsea 12 months ago.
Roy Beerens nearly got AZ off to the perfect start after just five minutes as he curled in an effort that looked like it may have been a cross but had Artur scrambling as it went just wide.
Benfica were enjoying the better of the possession but it was the Dutch side who were having the chances and Aron Johannsson brought a smart save from Artur when released by Beerens.
That led to two corners and, when the ball came out of the penalty box from the second of those, Steven Berghuis unleashed a thunderbolt which the goalkeeper once again did well to beat away.
The Portuguese side were looking dangerous with the ball despite their lack of clear-cut chances and Maxi Pereira had a chance to put them ahead but Celso Ortiz made an important block.
Ruben Amorim then went down in a heap and looked in considerable pain as he was helped off, with Andre Almeida being brought on to replace him.
Guilherme Siqueira went as close as Benfica had come so far as he jinked his way to the edge of the box but his shot went well over with a more ambitious Rodrigo volley heading the same way two minutes before the break.
But that was not to be the last chance of the half with Berghuis cutting in from the byline and unleashing a shot but Artur was equal to it.
AZ had by far the better of the first half and will have felt hard done by when they went behind four minutes into the second half.
Oscar Cardozo's shot was saved by Esteban but when the ball fell to Salvio on the edge of the box he did well to volley into an unguarded net.
The goal clearly increased the confidence of Jesus' men and Cardozo flashed a shot wide before Rodrigo's header brought a smart save from Esteban.
Ezequiel Garay then fired wide as Benfica continued to press but Salvio nearly put the ball in his own net with a header from a Nemanja Gudelj set-piece - but Artur was on hand.
Esteban was called upon with eight minutes to go to keep his side in it as Andre Gomes got a glancing header onto Lima's corner but the keeper made a good close-range save.
It was the home side who had the last chance through Beerens, who charged down the left and crossed for Johannsson - but the United States international missed the ball completely and it clattered into his standing leg.