Brazil joined hosts Argentina, their rivals in the previous two finals, in going out of the tournament at the same stage after Argentina lost on penalties to Uruguay on Saturday.
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Brazil dominated the 120 minutes of play which ended 0-0, creating a string of chances which Paraguay repelled with a mix of stubborn defending, some luck and a man-of-the-match performance from goalkeeper and captain Justo Villar.
The teams were down to 10 men each from the 13th minute of extra-time after a scramble for the ball by several players on one side of the pitch developed into a free-for-all with Paraguay defender Antolin Alcaraz and Brazil midfielder Lucas Leiva sent off.
The Brazilians, brilliant at times in open play, were dismal in the shootout with Elano, Andres Santos and Fred all firing their penalties wide while Villar saved from Thiago Silva.
Edgar Barreto missed Paraguay's first penalty but Marcelo Estigarribia and Cristian Riveros converted theirs.
"It was a match dominated almost entirely by Brazil. We had to take refuge a lot of the time at the back and, well, the penalties are a lottery which we took well and they failed with theirs," Villar said.
"You need more than will to win matches, you need goals and all Brazil lacked was goals," Brazil coach Mano Menezes told a news conference.
"Our opponents have not won a match [at the tournament]," he added after Paraguay qualified with three draws including 2-2 against Brazil in their group.
Brazil had the best moves of the first half. In the seventh minute, Robinho ran from the right across to the left and fed Pato whose pass back into the middle was only half-cleared with Neymar volleying the ball just over the bar.
They should have scored close to the half hour when Paulo Henrique Ganso passed forward to Robinho who threaded a good ball out right to the unmarked Neymar whose low shot went just outside the far post.
VILLAR SAVES
Left-back Andre Santos took a 33rd-minute free-kick, putting it low into the edge of the six-yard box where centre-back Lucio broke through but had his effort blocked by Villar.
Andre Santos shot over when set up by midfielder Ramires's diagonal pass from deep on the right as the first half wound down.
Brazil got back to business right away in the second half as Maicon set up Neymar for a shot that was scrambled away to Maicon, whose shot was also blocked.
Ganso had a brilliant low shot saved by Villar at the base of the near post in the 67th and five minutes later the goalkeeper blocked a point-blank effort from Pato.
Pato looked set to score in the 82nd when put through by Robinho bu
