The Baby Flying Fijians conceded the opening try after eight minutes in Santa Fe when first five Joaquin De La Vega Mendia spotted a mismatch in defence and got on the outside of lock Chris Minimbe to score in the left-hand corner.
The home side doubled their lead six minutes later after Caleb Muntz had missed a penalty goal attempt for Fiji.
Quick hands put fullback Ignacio Mendy into space down the right hand touchline, with the custodian stepping inside the final line of defence to give Argentina a 10-0 advantage at half-time.
Seconds into the second spell, number eight Juan Bautista Pedemonte crashed over for Argentina's third try before lock Etonia Waqa responded for Fiji two minutes later, busting through the defensive line and sprinting 25 metres to the tryline to cut the deficit to 15-7.
Fiji failed to to add to their score while Pedemonte spent 10 minutes in the sin bin, with Rodrigo Isgro Alastra scoring Argentina's fourth try to extend their lead to 13 points.
Ramiro Gurovich and Thomas Gallo also found the tryline to put the result beyond doubt with 12 minutes remaining.
Openside flanker Alivereti Loaloa managed a consolation try for Fiji but the match ended in disappointing fashion with substitute Anasa Qaranivalu sent to the sin bin before Argentina were awarded a penalty try in the final play.
Fiji, who lost their tournament opener 36-20 against defending champions France, play their final match in Pool A is against Wales on Thursday.