Four first-half goals powered Cerro Porteno to a commanding half-time lead on Wednesday, including a brace from Angel Romero.
Francisco Arce's men did allow Sol in, though, and the visitors to the Estadio General Pablo Rojas in Asuncion struck seven minutes after the break via Ignacio Mino.
Matias Corujo reinstated Cerro Porteno's four-goal buffer shortly after, but a quick-fire brace inside the final 10 minutes from Sol's Christian Ovelar would have had the hosts nervously looking over their shoulder.
But Romero wrapped up his hat-trick on 89 minutes, to send Cerro Porteno fourth - level on 21 points with Sol, but ahead on goal difference.
Libertad opened up an 11-point buffer atop the table, after beating Rubio Nu 1-0 on the road.
Olimpia were in second spot, but a 1-0 loss away to Sportivo Luqueno allowed Guarani, 2-0 winners at home to General Diaz, to become Libertad's closest challengers.
Cellar-dwellers 12 de Octubre fought back for a 1-1 draw at home to fellow strugglers 3 de Febrero, while Deportivo Capiata's hosting of Nacional Asuncion was postponed with the latter in Copa Libertadores action.
Asuncion sit in sixth spot, four points behind second-placed Guarani, but have two games in hand on all sides above them.
