Central defender Alejando Silva had given the Paraguayan side a 22nd minute lead with a shot from the edge of the box before midfielder Wilson Pittoni sent home fans into raptures with a priceless second goal three minutes into added time.
Atletico defender Richarlyson will miss next Wednesday's second leg in Belo Horizonte after he was sent off for a second bookable offence in the 89th minute but the biggest disappointment for the visitors was the performance of Ronaldinho.
The playmaker had a poor game for the tournament favourites with coach Cuca hauling him off after a little more than an hour to send on Guilherme, who scored a key equaliser in last week's semi-final, second leg against Newell's Old Boys.
"He wasn't good, He wasn't playing well and he's a player like any other," Cuca said of the talismanic Ronaldinho, who glared disapprovingly at the coach as he trudged off.
Despite the setback, Atletico will not be giving up hope of securing a first Copa Libertadores victory after they reached the final by overturning a 2-0 first leg deficit against Newell's of Argentina before advancing on penalties.
The Brazilian side's best chance came in the 77th minute when striker Jo was set up by Guilherme with a good chance for an equaliser but his effort was well saved by Olimpia goalkeeper Martin Silva with his foot.
"I think Olimpia played some good football against such good opponents as Mineiro," the Paraguayan side's coach Ever Almeida said.
Atletico president Alexandre Kalil said; "We have the most Argentine (passionate) fans in Brazil, we're going to turn this result around. The fans will pack the Mineirao.
"In these circumstances, the Mineirao has become the ideal stadium," added Kalil, who had originally complained about not being allowed to stage the second leg at Atletico's Independencia ground.
Organising body CONMEBOL ruled the 23,000-capacity Independencia was too small and ordered the match to be played at Belo Horizonte's newly refurbished World Cup stadium.
Meanwhile, last year's Libertadores winners Corinthians completed a 4-1 aggregate victory over Copa Sudamericana holders Sao Paulo to lift the South American Supercup.