Ramon Azeez was dismissed for a second bookable offence eight minutes into the second half to hand Granada a numerical advantage with just under half of the game remaining.
But, for the seventh time in the league this season, Joaquin Caparros' men drew a blank in front of goal and remain just above the relegation places.
Azeez can have no arguments over his red card as he crudely upending Manuel Iturra just after the restart as the Granada man attempted to scamper over the halfway line and launch a counter-attack.
Granada immediately attempted to punish Almeria as substitute Jhon Cordoba went close to breaking the deadlock twice in as many minutes.
Cordoba first steered Youssef El-Arabi's cross straight at goalkeeper Ruben from close range before he steered a header agonisingly wide.
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