The hosts took a shock lead in Asuncion when Jose Negreiros turned in Jonathan Fabbro's low cross in the 35th minute.
Six-times champions Boca were awarded a penalty in the 67th minute when Hugo Ibarra went down in the area, under a challenge by Elvis Marecos, but television replays clearly showed no contact was made and Juan Roman Riquelme looked almost apologetic as he celebrated after firing home the penalty.
Boca, who lead Group Two with nine points from three games, took full advantage as Martin Palermo and Rodrigo Palacio scored twice in the last 15 minutes to give them a flattering win.
Guarani are bottom after losing all three games.
Apart from Boca, Argentine clubs have been in miserable form in the tournament and their dismal run continued when San Lorenzo lost 1-0 at home to Paraguayan champions Libertad.
San Lorenzo defender Gaston Aguirre turned the ball into his own net five minutes after the restart to leave his side third in Group Eight with three points from four games.
Libertad lead with 12 points from four games, though they suffered a major fright when midfielder Vladimir Marin fainted during the second half.
He was given oxygen and taken off the field in an ambulance, interrupting the game for seven minutes, but regained consciousness and did not require hospital treatment.
Brazilian pair Sao Paulo and Cruzeiro both won to stay top of their respective groups.
Sao Paulo ground out an efficient if uninspiring 1-0 win away to Uruguay's Defensor Sporting thanks to a goal from striker Borges six minutes before halftime.
They lead Group Four with seven points from three games while Defensor are third with four.
Cruzeiro beat Bolivia's Universitario de Sucre 2-0 in Belo Horizonte with two second half goals from Wellington Paulista to pull five points clear at the top of Group Five.
Universitario are bottom with one point. Bolivian clubs have yet to win a game between them in the competition.
Unfashionable Colombian side Boyaca Chico went top of Group Seven with a shock 3-0 win at home to Universidad de Chile in Wednesday's other match.
Edwin Movil, Winston Giron and Juan Gilberto Nunez scored Boyaca's goals.
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