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.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
