And they repeated the trick with Hamilton's first-half try and the steady boot of Parks ensuring Scotland picked up their first series win on foreign soil in 50 years.
Scotland beat Argentina 24-16 a week ago without scoring a try but finally crossed the whitewash after three minutes when Hamilton squeezed through and Parks converted.
Felipe Contepomi reduced the deficit with two quick penalties moments later and Argentina nearly scored a try of their own but Hugo Southwell denied prop Rodrigo Roncero near the line.
Parks edged Scotland further ahead with a penalty shortly after but then proceeded to send two efforts wide.
Roncero was soon sin binned for an offence at the line-out but Scotland failed to make the most of it with a John Barclay charge pulled back for a forward pass.
Argentina flew out of the blocks after the restart and despite battling their way into Scotland's half only had a penalty from Martin Rodriguez to show for it.
The home side continued to press but saw their hopes of winning dealt a blow when Parks booted over another penalty to all but seal victory.