Silva headed home a late equaliser for Mineiro, which ensured the Copa Libertadores finished at 2-2 after two legs, and the 34-year-old central defender slotted 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 but second-half goals from Jo and Silva forced extra time and, while Olimpia held out under intense pressure from the hosts in the additional 30 minutes, the Paraguayan side missed two penalties to fall just short in the continental decider.
Jo started Mineiro's comeback in the 46th minute at the Estadio Governador Magalhaes Pinto when he took advantage of a botched clearance from Olimpia 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 like they might collect their fourth Copa 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.
Mineiro dominated extra time with a header hitting the bar, and Olimpia defender Herminio Miranda cleared a shot off the line with a well-timed interception.
But Mineiro would not be denied in the shootout with goalkeeper Victor saving Miranda's opening spot kick.
Alecsandro, Guilherme, Jo and Silva all converted their spot kicks for Mineiro before Gimenez hit the bar, sending the home side and their fans into raptures.
The victory ensured Mineiro's star playmaker Ronaldinho joined a small group of players to have lifted both the UEFA Champions League and Copa Libertadores' trophies.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.