The Pumas, fresh from their inaugural season in the Rugby Championship, dominated possession and territory under the roof at the Millennium Stadium and while it took them nearly an hour to break through the Welsh defence, once they had, the floodgates opened and victory was never in doubt.
Wingers Juan Imhoff and Gonzalo Camacho scored second-half tries for Argentina while fly-half Nicolas Sanchez converted both tries and kicked two drop goals and a penalty for a personal haul of 13 points.
Fullback Leigh Halfpenny kicked all the Welsh points with four penalties.
"We have been searching for this win for a long time as a group," Pumas captain Juan Martin Fernandez Lobbe told BBC Sport.
"We are so happy to be able to win against such a good team, the Six Nations champions...It's huge to get this win for this group, in this stadium, the best stadium in the world."
Expectations of a scrappy test match were realised early on as Argentina adopted a predictably direct and forward orientated approach.
Experienced centre Felipe Contepomi, returning to the Pumas side after missing the Rugby Championship, gave the visitors the lead after three minutes when he made Welsh lock Ian Evans pay for a high tackle by calmly slotting the resulting penalty from almost directly in front.
It would prove to be Contepomi's last significant act of the match, and possibly of his international career, as the 35-year-old was stretchered off the field with a knee injury after 12 minutes.
Halfpenny put Wales on the board soon after they went behind but Sanchez, promoted to fly-half ahead of Juan Martin Hernandez, who instead started at fullback, underlined Argentina's game plan as he slipped back into the pocket to snatch a drop goal and restore his side's three point lead.
It did not last long, however, and two more Halfpenny penalties ensured Wales took a slim 9-6 advantage into the break.
Argentina came out with more ferocious intensity in the second half, and after Sanchez's drop goal cancelled out Halfpenny's fourth penalty, they capitalised on their continued dominance in possession and territory.
Sustained forward pressure produced Argentina's first genuine try scoring opportunity of the match and they duly took it when influential openside flanker Juan Martin Leguizamon offloaded the ball to his captain Juan Martin Fernandez Lobbe who found a flying Imhoff.
With Halfpenny approaching, Imhoff stepped off the right foot to leave the Welsh number 15 stunned as he ran to score under the posts.
The try bred renewed confidence in Argentina and they had Wales on the ropes when more blunt forward play created surging momentum and Camacho benefited when the ball was spat out to the right and he dived to score in the corner.
Sanchez converted both tries and added a late penalty to ensure Argentina's second ever victory in Cardiff. It came exactly eleven years to the day since their first.
Wales have now lost their last four tests following their June tour of Australia and have little time to pick themselves up with Samoa, world champions New Zealand and Australia to come in the next three weeks.