Ever Hugo Almeida's men were beaten 4-3 on penalties by Brazilian outfit Atletico Mineiro in last week's Copa Libertadores final.
But Olimpia quickly put that result at the back of their minds, with a Ricardo Mazacotte double and Arnaldo Castorino's effort inspiring the hosts to victory.
Gustavo Toranzo scored a consolation goal for the visitors in the 57th minute.
Elsewhere on Sunday, Sportivo Luqueno and Deportivo Capiata also opened their campaigns with wins over Cerro Porteno PF and Sol de America respectively
Luqueno secured maximum points at the Estadio Felipe Gimenez thanks to first-half goals from Marcelo Ferreira and Sergio Escalante, while Fabio Escobar's 73rd-minute strike handed Capiata a 2-1 victory at Sol de America.
On Saturday, Cristian Martinez cancelled out Jorge Recalde's earlier effort as General Diaz and Libertad played out a 1-1 draw.
Meanwhile, Friday's fixtures saw Rubio Nu score twice in the final six minutes to snatch a 2-2 draw at home to Nacional Asuncion, while the match between Cerro Porteno and Guarani finished 1-1.
