Nishikori needed an hour and 41 minutes to see off the challenge of the fifth-seeded Dolgopolov, breaking the Ukrainian twice in the first set and once in the second.
The world number five is bidding to reach a career-high ranking of fourth this week, a feat which he will accomplish should he reach the final of the Acapulco event.
Standing in his way is fourth seed Kevin Anderson, who beat Viktor Troicki 3-6, 6-3, 6-3 earlier on Thursday.
Not for the first time this week the powerful South African had to come back from a set down to ensure his progression. Having failed to defend the only break point Troicki manufactured in the match, Anderson saw the first set slip away from him. However, he bounced back to break Troicki once in the second set and twice in the third as he marched into the final four.