Ajax dominated the first half of the game but could not recover from the blow Uruguayan striker Nunez beat goalkeeper Andre Onana to Alex Grimaldo’s free-kick.
Benfica will now appear in the last eight for the first time since 2016 after sending Barcelona packing in the group stage.
Sebastien Haller of Ajax had been hoping to score in an eighth consecutive Champions League game this season, but to no avail, the team lost the game.
Sebastian was upstaged by Nunez as Benfica’s own prolific forward found the target for the 26th time in all competitions since the start of the campaign.