In the play-off to decide the champions of the first phase of the season, neither side could trouble the scorers at Alajuelense's Estadio Alejandro Morera Soto.
That means whoever edges the second leg at Marvin Solano's Herediano on Sunday will be crowned Invierno champions.
Herediano are the current champions after beating Alajuelense in the second phase of last season 3-2 in the two-legged final.
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