Ever Banega curled in a free-kick before Sergio Aguero made it 2-0 after 36 minutes, with the Manchester City forward later taken to hospital as a precaution after fainting during half-time.
Leicester striker Kelechi Iheanacho started the recovery for the Super Eagles with another well-executed free-kick just ahead of the break.
Arsenal forward Alex Iwobi swept in an equaliser five minutes after the restart and another from defender Brian Idowu, on his debut, swiftly turned the match around.
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Iwobi netted a fourth with 17 minutes left to complete a remarkable comeback and leave Sampaoli facing more questions over the direction of his team on the road towards next summer's finals.
"It was a very difficult game to explain," said Sampaoli, who was without Lionel Messi after the Barcelona playmaker returned to Spain following the friendly with 2018 World Cup hosts Russia in Moscow.
"In the first half we could have been three or four nil ahead, but ended up at 2-1.
"Then in the second half, in just nine minutes with three long shots, they scored three goals. After this, the momentum was in favour of Nigeria.
"We did not have the energy of the first half and Nigeria's lead could have been extended further."
Sampaoli added at a press conference, quoted on the Argentina Football Federation website: " All these tour matches give us the opportunity to evaluate and draw conclusions.
"From this, we must draw a clear diagnosis of what happened for what is to come.
"Mental strength has a lot to do with the future, we can not neglect it.
"We must have the ability to know how to change difficult moments without going into madness."
Nigeria coach Gernot Rohr also intends to make the use of the build-up towards next summer's finals in Russia.
"Such matches are specially designed so that we can evaluate new players in the team," he said at a press conference.
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