Juan Sebastian Veron was suspended.
Three goals in ten early first half minutes were enough to win it for the Argies.
Argentina go top of the South American qualifying group.
The rain, strong winds and a tight Bolivian defensive scheme made things hard for the home team in the first 45 minutes.
But Marco Bielsa's side scored three times early on in the second half before cruising to a comfortable success.
Ten minutes after the break, Andres D'Alessandro opened the scoring with a free-kick, Crespo doubled the advantage six minutes later and then Pablo Aimar completed the rout.
"I liked the attitude we had to look for the victory at any time," said midfielder Christian Gonzalez. "Argentina may play good or bad, but you can't question our attitude."