As an amateur, Narváez represented Argentina at the 2000 Olympics, reaching the round of 16 of the super flyweight bracket.

He won the WBO world flyweight title on July 13, 2002 by a unanimous decision win over Adonis Rivas.

He defended the title against 15 different contenders such as Luis Alberto Lazarate, Andrea Sarritzu, Everardo Morales, Alexander Mahmutov, Reginaldo Martins Carvalho, Bernard Inom, Rexon Flores, Walberto Ramos, Brahim Asloum, Marlon Marquez, Carlos Tamara, Iván Pozo, Alejandro "Payasito" Hernández, Rayonta Whitfield and Omar Soto.

Narvaez faced Nonito Donaire on Oct. 22, 2011, at The Theater at Madison Square Garden at Bantamweight.

On 14 October 2017, Narvaez fought Nikolay Potapov who was ranked #2 by the WBO and #12 by the IBF at bantamweight.