Nunez stole the show in Heredia on Sunday as his side – who have played up to six league games less than other sides due to cup and continental commitments – posted their first win of the Torneo de Invierno season.
Herediano's run to the Copa Costa Rica semi-finals, and their ongoing involvement in the CONCACAF Champions League, has left them playing catch-up on their rivals.
But while they are on the bottom of the table for now, it is not likely to last long if Nunez can keep up his form.
Last season's Torneo de Invierno runners-up came from behind to win 4-2 at Isidro Metapan on Thursday in the Champions League, with Nunez scoring twice.
And he opened the scoring in the 26th minute before Jose Sanchez doubled Herediano's advantage on the stroke of half-time.
Nunez' second and third goals were sandwiched by an Aaron Navarro effort for Puma Generalena, but it was no more than a consolation as Antonio Michael Pedroza wrapped up the win with Herediano's fifth in second-half stoppage time.
UCR still top the table – some 15 points and five games ahead of Herediano – with a 3-0 home success against Uruguay.
Victor Coto, Olman Vargas and Josue Martinez all scored for the leaders.
Copa Costa Rica winners Cartagines are hot on UCR's heels, just two points adrift after a 1-0 triumph over Deportivo Saprissa.
Daniel Hernandez Astorga netted the game's only goal in the 48th minute.
Alajuelense maintained their unbeaten record with a 2-0 win over Carmelita on Saturday.
Belen Siglo XXI are without a win in four after a 1-1 home draw against Santos de Guapiles, while Perez Zeledon edged Limon 2-1.
