The defender ensured the game went to extra-time with a late equaliser before firing home what proved to be the decisive penalty as Cuca's side lifted their first-ever title
Leonardo Silva was the hero for Mineiro as he headed home the late equaliser that ensured the tie finished at 2-2 after two legs, and the 34-year-old defender then slotted home his side's fourth and final spot kick of the shootout before Olimpia's Matias Gimenez hit the bar, handing the Brazilians victory.
Mineiro started Wednesday's second leg two goals down, and after a goalless first-half, the tie appeared to be heading in Olimpia's favour.
However, Jo started Mineiro's comeback in the 46th minute at the Estadio Governador Magalhaes Pinto when he took advantage of a botched clearance and struck the ball on the turn past visiting goalkeeper Martin Silva.
The home side kept pushing for an equaliser but as the half wore on, Olimpia looked set to collect their fourth Libertadores title until Julio Cesar Manzur was sent off in the 85th minute. That decision gave Mineiro the momentum and, just two minutes later, the hosts drew level when Silva leapt highest to head Bernard's cross into the top corner of Olimpia's net.
The Brazilians dominated extra-time, with one header hitting the bar before Olimpia defender Herminio Miranda cleared a shot off the line with a well-timed interception.
But Cuca's side would not be denied in the shootout, with goalkeeper Victor saving Miranda's opening spot-kick before Alecsandro, Guilherme, Jo and Silva all converted. Gimenez then rattled the bar for the Paraguyans, sending the home support into raptures.
The victory ensured Mineiro's star playmaker Ronaldinho joined an elite group of players to have lifted both the Champions League and Copa Libertadores' trophies: former AC Milan trio Dida, Cafu and Roque Junior all secured the double, along with Inter defender Walter Samuel and Juventus striker Carlos Tevez.