Ebden was clinical in the opening stages, converting each of his break-point opportunities against the world number 26 to secure the first set 6-3.
The Australian soon jumped out to a two-set lead, dropping just one game en route to sealing the second set 6-1, despite less efficient statistics.
Nishikori was then able to come from behind in set three, breaking the Australian twice to win the set 6-4 and keep himself in the match.
The 22-year-old then made it back to back sets, breaking Ebden on three occasions to tie the proceedings at two sets apiece.
Nishikori completed his comeback in the final set with another 6-1 result, sending him into the next round.