Paraguay came from behind with a stirring second-half performance to beat Slovenia and clinch their place in the last 16.
A double strike by Nelson Cuevas and another by Jorge Campos led Cesare Maldini's side to a second-round meeting with Germany but they had to do it the hard way.
Acimovic scored just before half-time
Paraguay had Carlos Parades sent off after only 21 minutes for a second yellow card after a nasty challenge on Milenko Acimovic.
And Slovenia capitalised in first-half injury time to take the lead, after both goalkeepers had been tested.
Tottenham-bound Acimovic made room for himself on the right and cut inside, his cross-cum-shot from a narrow angle slipped through Chilavert's fingers and into the net.
Miran Pavlin tried a shot from the edge of the area which Chilavert was always going to get the better of.
We had to fight a lot in this match
Paraguay manager Cesare Maldini
With their numerical advantage, Slovenia tried to get the second goal which would have well and truly ended Paraguay's chances.
Acimovic hit the bar with a rasping shot while Milan Osterc also caused problems for Chilavert.
But a couple of Paraguay substitutions in the second half by Cesare Maldini helped pave the way to their victory.
After 66 minutes, substitute Nelson Cuevas, only on the field for five minutes, came in from the right to hit a left-footed shot past Dabanovic for the equaliser.
The goal seemed to boost Paraguay and seven minutes later, Jorge Campos got their second with a low shot from close range which beat Dabanovic.
Chilavert then hit a tremendous free-kick which was tipped onto the bar.
Worse was to follow for Slovenia when Nastja Ceh was sent off after 81 minutes.
Three minutes later, Cuevas grabbed his second with a rasping drive which hit the underside of the bar before going in.
Slovenia: Mladen Dabanovic, Zeljko Milinovic, Doni Novak, Ales Ceh, Milan Osterc (Senad Tiganj 77), Miran Pavlin (Mladen Rudonja 40), Rajko Tavcar, Milenko Acimovic (Nastja Ceh 63), Amir Karic, Sebastjan Cimirotic, Spasoje Bulajic.
Subs Not Used: Sasa Gajser, Marinko Galic, Aleksander Knavs, Dejan Nemec, Zoran Pavlovic, Goran Sankovic, Marko Simeunovic, Muamar Vugdalic. Sent Off: Nastja Ceh (81).
Booked: Pavlin, Karic, Rudonja, Milinovic.
Goals: Acimovic 45.
Paraguay: Jose Luis Chilavert, Francisco Arce, Carlos
Gamarra, Celso Ayala, Guido Alvarenga (Jorge Campos 54), Roque Santa Cruz, Roberto Acuna, Carlos Paredes, Julio Cesar Caceres, Jose Cardozo (Nelson Cuevas 61(Juan Carlos Franco 90), Denis
Subs Not Used: Richart Baez, Carlos Bonet, Diego Gavilan, Gustavo Morinigo, Daniel Sanabria, Pedro Sarabia, Estanislao Struway, Ricardo Tavarelli, Justo Villar.
Sent Off: Paredes (22).
Goals: Cuevas 65, Campos 73, Cuevas 84.
Referee: Felipe Ramos Rizo (Mexico).
MATCH STATS |
| Slovenia | Paraguay |
Corners (1st half) | 1 | 6 |
Corners (2nd half) | 0 | 3 |
Fouls committed | 19 | 13 |
Caught offside | 0 | 1 |
Shots on target | 10 | 12 |
Shots off target | 6 | 6 |
Hit woodwork (back into play) | 1 | 0 |
Yellow cards | 4 | 1 |
Red cards | 1 | 1 |
STOPPAGE TIME | |
First half - 2 mins | Second half - 3 mins |