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.
Victor Obinna converted a hotly-contested penalty 17 minutes later before Uche scored the third in the 40th minute, heading home unmarked at the back post after a strong run from Obinna and a perfect cross from Taye Taiwo.
"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.
Argentina, ranked fifth in the world, were handed an equally controversial penalty in the eighth minute of stoppage time and Mauro Boselli scored with the last kick of the match.
The absence of Lionel Messi and strict security around the stadium meant Abuja's 60,000-seater National Stadium was half empty.
