Twice before in 2011 and 2015 Paraguay had beaten Brazil at this same stage on penalties at the South American extravaganza.
Paraguay held out for a 0-0 draw for more than 40 minutes following the dismissal of Fabian Balbuena for a professional foul on Roberto Firmino.
Brazilian media had been almost in a state of paranoia before the match recalling the painful memories from Argentina in 2011 and Chile four years later when Paraguay produced stubborn defensive displays before snatching victory in the spot-kick lottery.
But it wasn't to be this time as Brazil goalkeeper Alisson saved Gustavo Gomez's opening spot-kick at the Gremio Arena in Porto Alegre.
Although Firmino dragged his effort wide, Derlis Gonzalez also fired past the post allowing Jesus, who missed a penalty in Brazil's last match, to be the match-winner.
The tournament hosts will face either rivals Argentina or Venezuela in semi-final in Belo Horizonte.