The world number 45 turned things around after trailing by a set and a 0-4 deficit in the deciding set, before winning 2-6, 6-4, 7-6 (5).
This is Eala's second consecutive tournament in the last eight, having reached the same stage last week at the Philippine Women's Open before being eliminated by eventual champion Camila Osorio.
Eala struggled in the first set as the Belarusian dictated play from the baseline and outscored the other player with a significant number of winners. Eala's serve also wavered several times under pressure.
In the second set, Sasnovich broke again first, but Eala immediately responded to keep the match alive.
