The Portuguese facet had not controlled a single attempt on track until Uruguayan striker Nunez beat goalkeeper Andre Onana to Alex Grimaldo's free-kick and headed in to silence the Johan Cruyff Arena.
Ajax, who had ruled the primary half, could not get over that blow and exit at the same time as -time European Cup winners Benfica look forward to Friday's draw for the sector-finals.
Having despatched Barcelona packing in the organization level, they may now seem within the remaining 8 for the primary time considering that 2016.
The Dutch facet's famous person striker, Sebastien Haller, were hoping to attain in an 8th consecutive Champions League sport this season having netted a great 11 desires in his first seven appearances in the competition.
Yet he was upstaged by means of the 22-year-old Nunez as Benfica's very own prolific forward determined the target for the 26th time in all competitions because the begin of the campaign.
A swashbuckling Ajax aspect had gained all six games inside the institution stage earlier than two times leading in opposition to Benfica within the first leg in Lisbon most effective to have to accept a 2-2 draw.
Haller, who has 32 dreams in general this season, had scored at both leads to that recreation and he had the ball inside the net inside the 7th minute here simplest for the effort to be dominated out because Dusan Tadic was flagged offside within the build-up.
Erik ten Hag's prolific side, who're top of the Dutch Eredivisie, checked out their excellent in the first half of but couldn't find a manner via as Steven Berghuis blasted over on the volley from just inside the container.
Ryan Gravenberch then unleashed a superb shot that was tipped over with the aid of Benfica goalkeeper Odisseas Vlachodimos, and that they did no longer look as threatening within the 2nd half of.
