The South Americans dominated the early stages at a half-full Olympic Stadium and Gonzalo Higuain put them ahead after 20 minutes with a curling shot after a sloppy error by Daniele De Rossi.
Argentina went 2-0 up when substitute Ever Banega fired home a fierce low shot from the edge of the area just three minutes after coming on at the start of the second half.
Lorenzo Insigne pulled one back for Italy against the run of play with a sweetly-struck curling shot from outside the area on 76 minutes, setting up a spirited finale by the hosts who finally exerted some pressure.
"All credit to this Argentina, we were playing a team of great quality, one of the strongest," Italy coach Cesare Prandelli told reporters.
"We made some mistakes at the back and lacked a bit of fight but we still did good things."
Italy and Argentina have won six World Cups between them and are both on course to qualify comfortably for next year's tournament in Brazil.
Italy, who have not beaten Argentina since 1987 and who were without injured striker Mario Balotelli, were often made to look sluggish but also had their chances.
Rodrigo Palacio went close for Argentina just before the break after a textbook counter-attack and substitute goalkeeper Federico Marchetti prevented Italy going three down in the second half when he scrambled away a close-range effort from Higuain.
Alessandro Diamanti hit the bar for Italy with a second-half free kick and one of the pluses for the home side was 22 year-old Insigne, who always looked lively after coming on as substitute and was delighted with his sweetly-struck goal.
"I always try to do this kind of shot in training and today it went well for me," said the Napoli striker.
(Reporting By Gavin Jones, editing by Ed Osmond)
