Nunez scored his first goal in the 16th minute, lifting a long ball out of defence over UCR goalkeeper Carlos Mendez to give Herediano a 2-0 lead.
The powerful 33-year-old striker also scored his team's fourth, dribbling through the middle of the visitors' defence with 10 minutes remaining and finishing into the bottom corner of the net.
Herediano moved to 20 points on the back of Saturday's victory, three clear of second-placed Alajuelense in the Primera Division table.
Deportivo Saprissa sit third with 16 points, while Limon are fourth, two points further back.
Herediano's opening goal was credited to Brazilian striker Leandrinho, who got his head to an in-swinging free-kick from the left in the sixth minute, although it looked as if a UCR defender contributed the final touch into the net.
Nunez doubled the home team's lead 10 minutes later before a rapid counter-attack in the 36th minute saw Leandrinho tee-up Francisco Calvo to score Herediano's third goal.
Herediano's final two goals came in the last 10 minutes with Nunez scoring in the 80th, while Anyelo Porras struck in the 88th, turning sharply in the box to slam the ball home.
Alajuelense failed to stay within a point of Herediano after being held to a scoreless draw at home by Saprissa, while Limon lost 2-1 at struggling Uruguay.
A brace from Jonathan Moya saw Uruguay to victory, as they moved three points ahead of bottom club Perez Zeledon.
Santos de Guapiles defeated Perez 3-0, while Belen Siglo XXI drew 2-2 with Cartagines and Puntarenas gave up a lead to complete a 1-1 draw with Carmelita.
