Oscar Ramirez's men have been playing catch-up after missing league fixtures due to CONCACAF Champions League commitments, but they have done so admirably - winning five straight games.
Ariel Rodriguez fired the visitors ahead on 11 minutes at the Polideportivo de Perez Zeledon, his effort bouncing past the home goalkeeper.
Roy Myrie had Perez Zeledon level on the half-hour mark, heading home from a corner, but Alajuelense led before the break - Armando Alonso heading home from a cross in the 45th minute.
Jose Ortiz's left-foot finish in the 86th minute all but sealed the three points, with Perez Zeledon's Fabrizio Ronchetti netting a 90th-minute consolation.
Ronchetti took a spot kick for the home side, and converted with a Panenka-style attempt.
Alajuelense still have three games in hand on leaders UCR, and trail them by just one point after winning seven of their eight games so far.
Deportivo Saprissa secured a 2-1 win over Belen Siglo XXI courtesy of a 90th-minute winner to Diego Estrada.
Saprissa consolidated fourth after the come-from-behind win, taking them to 19 points - seven behind UCR.
Herediano, in a similar position to Alajuelense with games in hand, enjoyed a 1-0 road win over cellar-dwellers Uruguay.
Antonio Pedroza scored the winner in the 82nd minute, to send Jafet Soto's men to their third win in seven.
Herediano sit in eighth on 12 points, with five games in hand on UCR.
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