Up two sets and a break in the third, the fifth-seeded Scot appeared to be cruising to victory but was stunned when Dolgopolov broke back and prevailed 7-3 in a tense tiebreaker.
The resurgence was to prove fleeting, however, as the world number 46 self-destructed early in the fourth set, falling back 4-0 to allow Murray to calmly serve out the 186-minute match on a chilly summer’s day at Rod Laver Arena.
“I had to go for my shots a little bit and on the tiebreakeer I was a little bit tentative,” the 23-year-old Murray said in a courtside interview.
“It was a very tough match and a really tough one to get my rhythm… Physically, I moved well. I’m gonna need a little bit more in the next match.”
Murray, beaten by Roger Federer for the title last year, will battle either Rafa Nadal or fellow Spaniard David Ferrer for a place in the final as he seeks to end Britain’s 75-year wait for a men’s grand slam champion.
Having mowed through his four previous opponents without conceding a set, Murray faced a far different beast against the unorthodox Dolgopolov, who stunned fourth seeded Swede Robin Soderling in five sets in the fourth round.
The Scot’s serve had been virtually impenetrable throughout Melbourne Park, but he found himself on the back foot from the very first game, and would have been down a break had Dolgopolov not sprayed a regulation forehand volley long.
Murray revels in punishing opponents for loose play and duly motored to 4-1 as the Ukrainian’s baseline blasts sailed past the lines on the way to notching up 77 unforced errors.
Dolgopolov quickly found his line, though, and blasted an outside forehand crosscourt to break back to 4-4, but the Scot upped the pressure at 6-5, whipping a down-the-line backhand winner to wrap up the 57-minute first set.
The blow seemed to drain the blood from Dolgopolov’s game, and the Ukrainian dragged himself listlessly around the court as his serve lost its venom in the second set.
He saved five set points to hang on at 5-3, but conceded the set on the sixth when Murray thundered a backhand return that seared the baseline.
The Ukrainian’s second coming punched the wind out of Murray, as he broke back to level at 3-3 and carry the match into a tiebreak.
Having dictated the play by keeping the Ukrainian wedged behind the baseline, Murray tensed up in the tiebreak, double-faulting then missing three consecutive shots to lose the set.
The crowd’s hopes of a sustained rearguard action slumped when Dolgopolov threw away two service breaks early and the Ukrainian ended up clubbing a forehand long to concede the match.