Alajuelense took the lead in the Clasico del Futbol Costarricense - the biggest fixture in the Primera Division - but Saprissa were level by half-time through Kendall Watson.
A second-half penalty to Carlos Saucedo and Juan Bustos' late goal, though, would see the hosts triumph.
The victory took Saprissa to 42 points at the top of the table, 10 clear of third-placed Alajuelense, while Herediano - who are second - dropped eight points behind the leaders following a 2-0 loss at UCR.
A goal-mouth scramble following a free-kick saw Alajuelense hit the front on the quarter-hour mark on Saturday with Alejandro Aguilar putting the ball in the net.
Saprissa equalised from a corner in the 36th minute as Watson headed home at the near post but the hosts had to wait until deep into the second half to take the lead.
The home side were given a penalty in the 77th minute and Saucedo made no mistake, sending Alajuelense goalkeeper Patrick Pemberton the wrong way to score.
Both sides finished the game with 10 players after Adolfo Machado and Jerry Palacios were red-carded in the 90th minute, while in second half stoppage time, Bustos capped off Saprissa's victory, volleying the ball into the net from a corner.
With UCR trumping Herediano on Sunday, Saprissa are in a strong position in the Primera Division.
Jason Scott and Lucas Gomez scored goals either side of half-time as UCR (29 points) won their second straight game to move within three points of Alajuelense in fourth.
Belen Siglo XXI sit a point adrift of UCR after their 2-1 win at Cartagines, while Carmelita (25 points) are sixth thanks to their 2-0 victory against Puntarenas.
In other results, Limon cruised past Uruguay 3-0 and Perez Zeledon defeated Santos de Guapiles 3-1 to move off the bottom of the table.
