Striker Joaquin Botero led the charge with a hat-trick which included a penalty, while Marcelo Martins, Didi Torrico and Brazilian-born Alex da Rosa shared the others at 3,600 metres above sea level.
Luis Gonzalez replied for the visitors who suffered their worst defeat since their 5-0 home loss to Colombia in 1993.
Argentina's misery was complete when substitute Angel di Maria was sent off after only seven minutes on the pitch.
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Maradona's team have 19 points from 12 games in the 10-team South American group while Bolivia have 12 points.
Argentina, who had won their first three games under Maradona without conceding a goal, looked breathless in the rarefied air and struggled with a pitch more suitable for grazing cattle than international football.
Their attempts to keep possession were thwarted as the ball bobbled around as if in a park game while Maradona, who last year supported Bolivia's campaign to be allowed to stage games in La Paz, looked on helplessly.
Bolivia employed their usual tactic of peppering the visitors goal with long-range shots, hoping the unusual flight of the ball would catch out goalkeeper Juan Pablo Carrizo.
Carrizo had already turned away one Martins shot before Bolivia went ahead in the 12th minute when the Ukraine-based forward scrambled the ball in after a mix-up in the defence.
Torrico hit the crossbar with a 30-metre effort as the ball flew around the pitch like a beach volleyball.
Lionel Messi nearly pulled one back in the 20th minute when he ran from the halfway line, played a one-two with Carlos Tevez and scooped the ball over Carlos Arias who just managed to tip it away.
Five minutes later, Luis Gonzalez levelled with a speculative 40-metre shot which bounced awkwardly six metres in front of goal and flew over Arias into the net.
Bolivia regained the lead eight minutes later when Javier Zanetti was judged to have fouled Da Rosa and Botero converted the penalty.
In the 45th minute, Arias sent a long goal kick up field to Botero who got behind the Argentina defence and pulled the ball back for Da Rosa to head the third.
Botero, who plays in the Mexican second division for Correcaminos (Roadrunners), headed Bolivia's fourth in the 54th minute.
He completed his hat-trick 11 minutes later when he latched on to a chipped ball forward and slipped a neat finish past Carrizo for his eighth goal of the qualifiers.
Di Maria, who came on for Maxi Rodriguez in the 57th minute, was sent off for a wild lunge at Ronald Garcia seven minutes later.
Paraguay scored in injury-time to draw 1-1 in Ecuador and stay top of the South American group while Brazil moved into second place after two goals from Luis Fabiano helped them to a straightforward 3-0 win at home to Peru.
Paraguay have 24 points while Brazil are three behind but only eight points separate them from eighth-placed Venezuela. Sandwiched in between are Chile (20), Argentina, Uruguay (17) and Colombia and Ecuador (14).
Substitute Cristian Noboa headed Ecuador ahead against Paraguay in the 64th minute in Quito, which is 2,800 metres above sea level.
Ecuador's Edison Mendez hit the crossbar and Paraguay defender Paulo da Silva was sent off, yet the resilient visitors left with a point when Edgar Benitez volleyed home in the second minute of injury-time.
"It was a fair reward because we deserved to take something from here," said Paraguay coach Gerardo Martino, whose side are on course for a fourth successive World Cup.
Brazil had little trouble in overcoming demoralised, table-propping Peru in Porto Alegre.
Luis Fabiano put them ahead with an 18th minute penalty after a foul on Kaka and added another nine minutes later.
Midfielder Felipe Melo scored the third in the 64th minute of a hopelessly one-sided game.
Chile managed to hold Uruguay to a goalless draw at home in Santiago despite having midfielder Mauricio Isla sent off in the 34th minute.
Uruguay attacked throughout the second half, finishing the game with four strikers, but were unable to force the winner.
"I think we lost two points," said Uruguay coach Oscar Washington Tabarez.
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