The world no.57 Nalbandian set up a secound round encounter with the German Florian Mayer.
Nalbandian, whose highest ranking was no.3, won this event in 2005 when beating Federer in the final.
Bernard Tomic of Australia played a tough match against the South African Kevin Anderson, winning in three sets 7-6 (5), 6-7 (4), 6-3. Tomic will play American Fish for a place in the third round.
Guillermo Garcia-Lopez of Spain defeated Somdev Devvarman of Thailand 6-4, 6-3 and his next opponent will be the top seed Spaniard Nadal.