The new Napoli signing put Cesare Prandelli's men to the sword with a goal and an assist for Ever Banega, while Lorenzo Insigne grabbed a consolation for the hosts
The Napoli striker troubled the hosts' defence on several occasions and deservedly finished the evening with a goal and an assist before being replaced after 60 minutes.
Argentina substitute Ever Banega doubled the advantage after half-time.
Lorenzo Insigne grabbed a consolation for Italy with a terrific curling effort with 15 minutes remaining, but, the home side, who had an offisde goal disallowed, could not find an equaliser.
The visitors were brighter initially, with Higuain looking particularly threatening in the opposition box. He had a shooting opportunity as early as the third minute but his tame effort was easily held by Gianluigi Buffon.
Italy's slow start was deservedly punished five minutes later. Marco Verratti gifted possession to Erik Lamela 35 yards from the Azzurri's goal and his pinpoint pass with the outside of his boot found Higuain in the box, who cut inside De Rossi to fire past Buffon.
The setback sparked Cesare Prandelli's men into action but they failed to carve out clear-cut opportunities, despite having claims for a penalty turned down.
Antonio Candreva was a real thorn in the Argentina defence, first delivering a cross that just evaded Pablo Osvaldo's outstretched boot before a teasing ball into the box was met by Claudio Marchisio, who inexplicably miskicked his effort straight to Albiceleste goalkeeper Mariano Andujar.
And they were nearly punished for their wastefulness when Angel Di Maria picked out Rodrigo Palacio at the back post, but the Inter forward failed to connect properly.
Lamela was surprisingly withdrawn at half-time to be replaced by Banega, but the decision was almost immediately justified with the substitute doubling the advantage in the 49th minute.
Higuain picked up the ball on the left-hand side of the box and laid into the path of the on-rushing Banega, who took one touch before striking firmly across Buffon into the left-hand corner.
Buffon was replaced in the 55th minute by Federico Marchetti and the goalkeeper was called into immediate action to make a fantastic double save.
Italy then had the ball in the back of the net in the 68th minute through Alberto Aquilani but the linesman raised his flag for offside.
However, with 15 minutes remaining, the home side did reduce the deficit when Insigne hit a sublime curling effort into the top right-hand corner from 20 yards.
Italy continued to push for the equaliser but they once again had Marchetti to thank as he produced a stunning save from Fernandez's bending shot in the 89th minute.
Argentina head into their World Cup qualifier with Paraguay in September full of confidence, while Italy will take heart from a spirited performance as they host Bulgaria and Czech Republic in the same month as they look to seal qualification to Brazil in 2014.