Brazil will face either Venezuela or Argentina, for the tournament's semifinals. Brazil had been eliminated by Paraguay the last two times the teams met in the Copa America quarterfinals, in 2011 and 2015, both times in penalty shootouts.
Goalkeeper Alisson made a save and Gabriel Jesus scored the decisive penalty as Brazil defeated 10-man Paraguay 4-3 in a penalty shootout to reach the semifinals of the Copa América on Thursday.
Alisson dived to his left to stop the initial penalty taken by defender Gustavo Gómez, and Gabriel Jesus sealed the victory to lead Brazil to its first semifinal appearance in the South American tournament since 2007.
Brazil will face either Venezuela or Argentina, which play on Friday in Rio de Janeiro.
Derlis González also missed from the spot for Paraguay, while Roberto Firmino failed to score for Brazil.
Both players sent their shots wide.
Willian, Marquinhos and Philippe Coutinho converted their penalties for Brazil, while Miguel Almirón, Bruno Valdez and Rodrigo Rojas netted for Paraguay.
Gabriel Jesus had missed a late penalty in Brazil's 5-0 rout of Peru in its last group game, but calmly found the net with his shot from the spot as Paraguay goalkeeper Roberto "Gatito" Fernandez went the other way, igniting the Brazilian crowd of more than 48,000 at the Arena Gremio.
"I was confident, I knew that if I took the penalty the way I'm used to taking it, I would have more chances of scoring," Gabriel Jesus said.
"I was upset after the other match because I didn't take the shot my own way. This time I waited for the goalkeeper to move and just sent the ball the other way."
Gatito had been key in regulation as the visitors held on to a 0-0 draw despite having a defender sent off in the 58th minute. In the Copa America quarterfinals, extra time is not played and the match proceeded straight to penalties.
Brazil had been eliminated by Paraguay the last two times the teams met in the Copa America quarterfinals, in 2011 and 2015, both times in penalty shootouts.
González, who also missed a penalty in Paraguay's 1-1 draw against Argentina in the group stage, had scored the decisive goal in the 2015 shootout. He was one of the five players back from that team that eliminated Brazil.
Paraguay played with 10 men after Fabian Balbuena was sent off for a foul that was initially called a penalty kick but was reversed after video review determined the foul happened outside the area.
Brazil controlled possession but struggled to create scoring opportunities against Paraguay's solid defensive system.
The visitors had one of the best chances of the first half when González's close-range shot was saved by Alisson.
Brazil pressed nearly full-time after Balbuena was sent off, but couldn't capitalize on its many opportunities. Gabriel Jesus, Coutinho, Everton and Firmino all missed great chances in front of the goal.
Fernández made a great reflex save on a close-range header by Alex Sandro near the end of the match, and in the 90th Fernández could only watch as a low shot by Willian struck the post.
Despite reaching the semifinals in 2015 and finishing runner-up in 2011, Paraguay has won only one of its last 21 matches in the Copa América, taking advantage of penalty shootouts to advance.
Paraguay reached the last eight this year with only two points, finishing as one of the two best third-place teams from the three groups.
Paraguay and Brazil failed to make it out of the group stage in the 2016 Copa America.
An eight-time South American champion, Brazil has won the tournament all four previous times it hosted the event, the last time in 1989.
Brazil's Neymar, dropped from the squad because of an ankle injury sustained just before the tournament, watched from the tribunes at the Arena Gremio.