Ike Uche scored twice but the handsome victory margin was tempered by the fact Argentina played with just two players who are in their provisional squad for the upcoming Copa America.
A 10th-minute goal from Uche began the rout as Nigeria rolled over listless opponents who seemed to wilt quickly in the steamy conditions.
"We knew Argentina had good players and we knew we had to score early to have any chance. This is a big morale booster for us," Uche told SuperSport television.
"Let's not take anything away from the importance of this win," added Nigeria captain Joseph Yobo.
Emanuel Emunike crowned the night with a deft lob over the goalkeeper's head as Argentina's defence was caught flatfooted again eight minutes into the second half.
The absence of Lionel Messi and strict security around the stadium meant Abuja's 60,000-seater National Stadium was half empty.
