Neri Pumpido's Olimpia failed to win at home for a fourth straight league fixture at the Estadio Manoel Ferreira in Asuncion but fought back late to secure a 1-1 draw against Mario Jacquet's strugglers.
Cecilio Dominguez's 50th-minute goal had seemingly put Sol on their way to breaking their winless run in road matches.
But Sol's dry away spell extended to 11 matches, when Olimpia's Carlos Guerreno smashed home the remnants of a save from opposition goalkeeper Roberto Acosta.
Libertad made the most of Cerro Porteno's fixture with Guarani being postponed, moving clear in first place after a 3-0 win at Rubio Nu.
Rodrigo Lopez put Pedro Sarabia's men ahead just prior to the half-hour mark, before two second-half penalties - one to Lopez, the other to Jorge Gonzalez - saw them to the three points.
