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Sevilla midfielder Ever Banega and Manchester City striker Aguero fired Argentina, playing without the rested Lionel Messi, into a 2-0 lead after 36 minutes.
But Leicester City striker Kelechi Iheanacho pulled one back on the stroke of half-time before Iwobi netted a second-half brace either side of a goal from Brian Idowu to shock the South Americans.
Local media later reported that Aguero was transported to hospital after fainting at half-time, with the forward undergoing medical tests as a precaution.
“We played really well in the first half but something went wrong after the interval,” Argentina head coach Jorge Sampaoli said. “We just failed to convert our chances today.
“I’m concerned that we cannot find a worthy replacement for Messi.”
Nigeria boss Gernot Rohr praised his team’s resolve after the three-time African champions had looked doomed to defeat.
“There were two completely different halves. The opening period was very hard. One could believe the match was already over after Argentina scored their second goal,” said Rohr. “But we managed to perform a comeback.
“After we scored we rearranged our play in the break and performed much better in the second half. My players are mentally strong, they showed strong will. I’m very happy with their perforance.”
Argentina, who beat Russia 1-0 in Moscow on Saturday at the ground that will host next year’s World Cup, left Messi out of Tuesday’s friendly following an agreement with Barcelona.
Banega delivered the opening goal on 28 minutes with a well-struck free-kick after Nigeria goalkeeper Daniel Akpeyi was penalised for a handball outside his area.
Argentina promptly doubled their advantage when Aguero, who scored the late winner over Russia, converted a right-wing cross by Cristian Pavon, the Boca Juniors winger making his first international start.
But Nigeria, who went unbeaten throughout their World Cup qualifying campaign, refused to surrender and Iheanacho halved the deficit before the interval with a 25-yard free-kick.
Iheanacho then found an unmarked Iwobi who equalised from close range on 52 minutes, with Amkar Perm defender Idowu drilling Nigeria into a 3-2 lead moments later.
Argentina’s attempts to claw their way back into the match were ended when Iwobi grabbed his second goal on 73 minutes, taking a pass from Ahmed Musa and hammering home to seal just a second win over the two-time World Cup winners in eight meetings.
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