A surprise signing for the Peruvian club during the close season, Solano headed home in the 62nd minute after coming on as a halftime substitute to wipe out Manuel Maciel's first-half opener for Libertad in Asuncion.
However, the former Newcastle United, Aston Villa and West Ham United player's joy was short-lived when Juan Samudio struck an 83rd minute winner for Libertad, Paraguayan champions four times in a row, in the Group Eight game.
Striker Andres Silvera scored twice as Argentina's San Lorenzo, semi-finalists last year, routed Mexican side San Luis 4-1 in the same group in Buenos Aires.
Silvera scored both his goals from headers in the first 20 minutes before Gonzalo Bergessio added another to give the hosts a 3-0 halftime lead.
San Luis defender Oscar Mascorro put through his own goal three minutes after the re-start and Victor Lojero notched a consolation for the visitors.
In another Argentina-Mexico clash, striker Jose Sand scored with the last kick of the game to earn Lanus a 1-1 draw at home to Guadalajara in Group Six.
Sergio Avila had given Guadalajara, Mexico's most popular club, the lead in the 33rd minute.
