Although they grabbed the only tries of the game through Gonzalo Tiesi and Juan Manuel Leguizamon, Scotland's back-row won the battle of the breakdown giving Parks the platform to boot the visitors to a morale-boosting victory,
But they were on the backfoot almost immediately when Felipe Contepomi, who missed the November international between the teams, started a counter attack that saw former Harlequins centre Tiesi go over in the corner,
Contepomi missed the conversion and then swapped penalties with Parks before Argentina fashioned their second try albeit in controversial circumstances.
Leguizamon latched onto Agulla's pass but despite appearing to be hauled down just short, the television match official ruled he had crossed although Contepomi failed to rub salt in the wounds with a missed conversion.
Despite trailing 13-6, Scotland then enjoyed their best period of the half with Leguizamon in the sin bin and Parks responded with a penalty and drop goal to bring the visitors to within one point.
They finally edged ahead in the 53rd minute courtesy of a Parks penalty which was soon followed by another three points to take Scotland out to 18-13.
Parks' exquisite drop goal was cancelled out by Contepomi's penalty but fittingly it was the former Glasgow fly-half who had the last word to wrap up the win.