The Napoli striker troubled the Italy defence on several occasions and deservedly finished the evening with a goal and an assist before being replaced after 60 minutes.
He grabbed the first goal of the night in the first half after a terrific pass from Erik Lamela before supplying an accurate pass into the path of Ever Banega to double the advantage just after half-time.
Lorenzo Insigne grabbed a consolation for Italy with a terrific curling effort with 15 minutes remaining, but the home side could not find an equaliser.
Italy were without Mario Balotelli, who missed the game through injury, with Roma striker Pablo Osvaldo replacing him, while Daniele De Rossi started the game in an unfamiliar centre-back role for the home side.
Alejandro Sabella's side had injury woes of their own with Barcelona star Lionel Messi unavailable. His absence gave 21-year-old Roma winger Lamela the opportunity to showcase his talent.
The away side made the brighter start 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 were struggling to find their rhythm and only had a blocked effort from an Emanuele Giaccherini strike to show for their efforts in the opening 15 minutes.
And their slow start was deservedly punished five minutes later. Marco Verratti gifted possession to Lamela 35 yards from Italy's goal and his pinpoint pass with the outside of his boot found Higuain in the box and he cut inside De Rossi to fire past Buffon.
Italy manager Cesare Prandelli will have been disappointed with the amount of room afforded to the former Real Madrid striker.
The setback sparked Italy into action but they failed to carve out clear-cut opportunities, although they had legitimate claims for a penalty when Giorgio Chiellini was dragged to the floor by Napoli defender Federico Fernandez from a free-kick.
Chiellini was once again involved when he narrowly headed Antonio Candreva's corner over the crossbar.
Candreva was becoming 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 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 was sliding as his effort went over the crossbar as the match headed for half-time.
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. Higuain pounced on a loose ball in the box that was parried into the path of Palacio, who only had to guide into the empty net but was denied by a stunning recovery save from Marchetti.
Italy then had the ball in the back of the net in the 68th minute when Alessandro Diamanti's free-kick was well saved by Andujar. The rebound was eventually put in by Alberto Aquilani but the linesman raised his flag for offside.
But 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 now who head into their FIFA World Cup qualifier with Paraguay in September full of confidence, while Italy will take heart from a spirited performance as they host Bulgaria and the Czech Republic in the same month as they look to seal qualification to Brazil in 2014.
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