Striker Nelson Haedo scored just before the half hour to secure Paraguay's place in South Africa next year, sending Diego Maradona's 10-man team crashing to a third successive qualifying defeat and their fourth loss in six qualifiers.
Paraguay climbed to second in the South American group on 30 points, with only goal difference separating them from leaders Brazil, who have a home game against Chile later on Wednesday.
Argentina, in grave danger of failing to qualify, dropped out of the top four automatic berths, their place taken by Ecuador. They occupy fifth place which would send them into a two-leg playoff against the CONCACAF's fourth-placed team.
"I'm not afraid of the critics," Maradona told a news conference. "I will keep on going and do my work.
"Paraguay played very well with Cabanas and Haedo. They kept the ball from us (up front) and we couldn't resolve that in the first half."
Haedo exchanged a one-two with midfielder Edgar Barreto in a flowing attack that scythed through the Argentina defence before fellow striker Salvador Cabanas set him up to score with a low shot past diving keeper Sergio Romero and inside the far post.
Argentina lost midfielder Juan Sebastian Veron, one of their better players in a poor team performance, eight minutes into the second half when he was sent off for a high tackle, his second bookable offence.
LUCKY START
Luck looked to be smiling on Argentina when two earlier efforts from Paraguay came back off the woodwork.
Haedo's shot from the left in the eighth minute was turned onto the post by Romero and midfielder Jonathan Santana hit the bar in the 23rd.
As in their 3-1 home defeat by Brazil on Saturday, Argentina played into Paraguayan hands with their short-passing game attempting to work their way through the middle of the defence.
Lionel Messi, a key forward whenever he plays for Barcelona, struck a forlorn, isolated figure, largely kept out of the Paraguay box by a well organised defence.
In a last-ditch bid to force an equaliser, Maradona sent on ageing striker Martin Palermo and centre back Rolando Schiavi, who became Argentina's oldest new cap at 36 years and seven months, in the final quarter of the match.
The pair almost combined for an injury time goal when Schiavi headed down a cross into the box and Palermo just failed to get a toe to the ball to turn it in.
"It's a tremendous joy for the Paraguayan people to qualify against Argentina," Haedo told a pitch-side TV reporter.
Paraguay goalkeeper Justo Villar said: "We just didn't let them play in the second half. We blocked them out."
Defender Paulo da Silva added: "Our forward line has improved. We have taken a very important step, getting three points that take us to South Africa."
After the final whistle, the Paraguay players hugged in a circle in the middle of the field in prayer, standing on a giant flag with their red and white colours covering the whole pitch.
