Perez had not won since the opening round of the campaign and after going behind on the stroke of half-time, the cellar-dwellers looked set for yet another disappointing day.
But with a stroke of luck, the San Isidro-based club struck back in the second half with an own goal from UCR defender Jason Scott sending Perez level before Jose Sanchez scored three minutes later to give them a lead they would not relinquish.
While the win was not enough for Perez to rise above bottom spot in the table, Daniel Casas' men did move within a point of second-bottom Puntarenas.
Perez have 10 points from 13 games, while Puntarenas (11 points) sit just behind Belen Siglo XXI (12).
Also on Sunday, Cartagines came from behind to draw 1-1 with Limon, while on Saturday, Puntarenas came from behind to draw 3-3 with Santos de Guapiles.
Deportivo Saprissa (28 points) remain first in the table despite not playing over the weekend, while second-placed Herediano have 27 points.
