Nacional headed into the Clausura game unbeaten in four – with three of them wins – but had no answers for the dogged hosts.
Sol's only previous league triumph of the season came last month but they returned to the winners' list thanks to Alfredo Mazacotte's 69th-minute goal.
Midfielder Mazacotte, who joined from Rubio Nu in July, has already scored three goals for his new club.
Libertad, who won through to the last 16 of the Copa Sudamericana on Wednesday, kept up their good form with a 2-0 home win against 12 de Octubre.
Libertad's win – also registered on Sunday – came thanks to second-half strikes from Jorge Gonzalez and Dionisio Perez.
League leaders Olimpia also left it late before securing their fourth win in five matches in a 2-0 success at Rubio Nu.
Cristian Ovelar opened the scoring 13 minutes from time before Carlos Acuna sealed their win.
Cerro Porteno gave themselves a boost before a big Copa Sudamericana clash with a 4-0 home rout of Sportivo Luqueno on Saturday.
Jose Maria Ortigoza netted twice in the second half, while Bruno Valdez and substitute Rodolfo Gamarra also scored.
Cerro trail Ecuador's Independiente 1-0 after the first leg of their last-32 Sudamericana fixture but they will host Tuesday's return clash.
In other results, 3 de Febrero won 3-2 at Deportivo Capiata on the back of a Cristian Colman hat-trick, while General Diaz and Guarani played out a 1-1 draw.
