British Murray, who is still chasing his first major title, won 7-5, 6-3, 6-7 (3-7), 6-3 in three hours and six minutes to set up a semi-final date with Ferrer.
Although ranking as world No. 46, Dolgopolov did not play bad and has gave Murray pressure throughout the match. The Ukrainian had knocked out world No.4 Robin Soderling in the previous round, and on Wednesday became the first player this year to keep Murray on court for more than two hours.
"It was very tough, every point was different, he hits, just different," Murray told reporters in Melbourne after the match.
"He came back at me well in the third set, but I did well in the end. I had to go for my shots a little bit more, I was a little bit tentative in the tiebreak, so went for my shots a bit more and that settled me down. It was a tough match, and a good one to get through."
"Physically I'm doing well on the court, but I'm going to need it a little bit more in the next match."
In women's draw, Second seed Russian Zvonareva, a finalist at the past two Grand Slam events - Wimbledon and the U.S. Open, on Wednesday took control of the match capitalizing on the nerves of her opponent, Czech No.25 seed Petra Kvitova, to win 6-2 6-4 in just 75 minutes.
Third seed Clijsters also comfortably banished Polish No.12 Agnieszka Radwanska 6-3 7-6 (7-4).
Zvonareva will face a tight game against Clijsters in the semis finals.
"I have to make sure I prepare myself well for the match, I don't over train, I stay fresh, stay focused on that match," Zvonareva told reporters in Melbourne. "I definitely will try to take positives from those matches when I beat her and try to think over again, okay, why I lost so quickly in the final, just try to avoid those moments."
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