The defensive midfielder headed a corner kick into the net, 25 minutes into the match.
Lekic doubled the lead four minutes later, just a minute before Granada's Rico pulled one back.
The Iranian national team's captain fellow defensive midfielder Punal received his marching orders for his second booking 16 minutes from time, but Osasuna held on to the narrow win.
Nekounam will now join Iran's national team for the World Cup qualifier against Qatar on Wednesday.
His clubmate and compatriot Masoud Shojaei is still sidelined injured and probably will not return to the pitch before the next season, therefore also likely missing Iran's third round qualifiers in June.
Osasuna - Granada 2:1 by FootballKing1992