Esteban Granados and Victor Nunez put Herediano 2-0 up after only 15 minutes as the away side dominated the early exchanges.
Belen Siglo tried to work their way back into the match but Jose Cancela's second-half brace sealed the three points for Herediano.
Bryan Vega did get a consolation goal for the home side with six minutes to play.
Alajuelense missed an opportunity to go level with Herediano, as they went down 1-0 at Uruguay.
A spot-kick from Uruguay's Johan Condega on the stroke of half-time was enough to seal their first win of the campaign.
Paulo Jimenez's brace saw Cartagines jump to second position with a 3-1 triumph at Limon.
Jimenez scored either side of Steven Calderon's equaliser for Limon with Cartagines' Leandro Silva sealing the three points on 70 minutes.
In other matches, Carmelita drew 2-2 with Deportivo Saprissa, UCR overcame Perez Zeledon 2-1 and there was a 2-2 draw between Puntarenas and Santos de Guapiles.
