A stunning strike from Alejandro Silva, and a late free-kick from Wilson Pittoni, was enough to get the job done on Wednesday, meaning Brazilian club Atletico have it all to do in Belo Horizonte.
Olimpia took the lead in the 23rd minute with a goal of the highest quality.
Silva picked up a short pass from Pittoni near the right wing and set off on a mazy run towards goal.
He launched a ferocious, low left-footed strike from just outside the box that had Atletico goalkeeper Victor well beaten and came off the inside of the post to open the scoring.
Silva was so excited that he took his shirt off to celebrate the goal, drawing a yellow card from referee Nestor Pitana, and he will now miss the second leg in Brazil next Wednesday.
Atletico coach Cuca replaced the misfiring Ronaldinho with Guilherme just after the hour mark, but the move did not have the desired effect.
With the match entering the final 10 minutes, Olimpia substitute Juan Ferreyra forced an outstanding save from Victor, and Fredy Bareiro somehow missed the follow-up from point-blank range.
Bareiro missed another good chance with five minutes remaining, when he charged into the box but blasted his left-footed effort high and wide.
Atletico defender Richarlyson was sent off in the 90th minute for his second bookable offence.
The home side had to wait until the fourth minute of stoppage time to double their lead.
Olimpia were awarded a free-kick just outside the box, and Pittoni stepped up to curl it past Victor with the last kick of the game, although the 'keeper was hard done by, with Atletico substitute Alecsandro getting in his way.
The goal sent the bulk of the crowd at the Estadio Defensores del Chaco into pandemonium, and the Paraguayan club are well placed in their bid to land their fourth Copa Libertadores title.