Paraguay had never before won a World Cup qualifier in Argentina, but a missed penalty from Sergio Aguero gave them three points in Cordoba.
Sergio Aguero failed to convert a penalty as Argentina suffered their first home defeat in a World Cup qualifier against Paraguay, losing 1-0 in Cordoba.
Having declared himself fit despite sustaining a calf injury during training, Aguero failed to make his presence count when he had his spot-kick saved by Paraguay goalkeeper Justo Villar - who was making his first start since this year's Copa America.
It proved a pivotal moment, with Argentina already trailing to Derlis Gonzalez's counter-attacking opener in the first half, the winger exploiting a lack of pace in an opposition defence to which Edgardo Bauza had made three changes following the 2-2 draw against Peru last time out.
Paraguay sat on that goal, inviting pressure from the hosts, who struck the post through Angel Di Maria in the first half and had a Marcos Rojo goal controversially ruled out for offside due to Gabriel Mercado's positioning after Aguero spurned another second-period opportunity.
Argentina, without star and captain Lionel Messi due to a groin injury, were unable to break down Francisco Arce's side and subsequently drop out of the automatic qualification spots in the CONMEBOL section following a third match without a win.
Paraguay, meanwhile, move to within one point of Bauza's fifth-placed team, giving their hopes of securing a place in Russia a huge boost.
The visitors came close to an opener in the seventh minute when Gustavo Gomez sent a diving header wide following Oscar Romero's free-kick from the left.
Paraguay only had to wait 11 more minutes to make the breakthrough, though, and it came following a rapid counter-attack.
Angel Romero released Gonzalez down the right who charged into the area with left-back Rojo nowhere to be seen, drilling beyond Sergio Romero at his near post.
Di Maria came close to restoring parity midway through the half when his left-footed drive from the edge of the box clipped the base of the post and went behind, while Rojo sliced a glorious opportunity over in the 26th minute.
Paraguay sat back and allowed Argentina to control possession, but further breaks saw Sergio Romero tested by long-range efforts from Oscar Romero and Angel Romero.
The hosts were gifted a chance to equalise at the start of the second half when a header from Gonzalo Higuain struck Paulo da Silva's arms inside the box, but Villar dived low to his left to deny Aguero from the subsequent penalty.
Aguero attempted to rectify his error two minutes later but after surging through the heart of the defence his poorly placed shot was blocked by Villar.
Rojo thought he had restored parity after Villar failed to claim a left-wing free-kick from Ever Banega, only to turn and see the assistant referee with his flag raised for a controversial offside.
Argentina continued to dominate but Higuain was unable to poke home Di Maria's low cross in the 64th minute, while substitute Paulo Dybala had a 20-yard drive batted away by Villar as Paraguay clung on to an important three points.