Brazil, five times world champions, had needed only to draw against their less illustrious neighbours in their last game of the South American qualifying tournament but were instead sunk by a 32nd-minute goal scored from rival captain Jose de Vaca.
Paraguay will thus join Argentina, who qualified with a game to spare, as South America's Olympic representatives.
Paraguay finished the four-team final stage with six points alongside Argentina, who were playing their final game against hosts Chile later Sunday. Brazil have three points and Chile none.
Brazil have always taken Olympic soccer seriously and see the gold medal as the one item missing from their trophy cupboard.
Coach Vanderlei Luxemburgo lost his job with the senior team after failing to take Brazil's Olympic squad beyond the quarter-finals in Sydney four years ago.
This time former Paris St Germain defender Ricardo Gomes took charge solely of the under-23 team and is almost certain to be axed in turn.
Brazil, whose squad includes five members of the Santos team which won the Brazilian championship in 2002, had beaten Paraguay 3-0 in the first stage of the tournament.
They fielded four attackers in the second half but were unable to break down a typically stubborn Paraguay defence and also found goalkeeper Diego Barreto in inspired form.
The closest Brazil came was when Dudu Cearense sent a shot agonisingly wide with five minutes to play.
