The Bulgarian came through 6-3 6-2 in just over an hour.
Dimitrov's biggest weapon was his serve as he found the corners time and time again.
He followed it up with some excellent ground strokes and rarely gave the Ukrainian any chances during the match.
Dimitrov has continued his recent form, after winning his first ATP title in Stockholm last week.
He will now face Roger Federer for a place in the semi-finals.