The third-round opponents started off the match evenly, with games going by the way of serve and neither being able to force a breakthrough in the early stages of the contest.
The first break of the match eventually came for Dolgopolov, who took the lead over his 19-year-old opponent.
Despite going a set down, Tomic managed to impose his game on the Ukrainian and take a 3-1 lead in the second set. However, the lead was short-lived as Dolgopolov fought back to level the set at 3-3.
While the 23-year-old Ukrainian tried to take a two-set lead, the Australian continued to push and force a tie-break. Despite a tight contest, the teenager comfortably cruised through the tie-break on 7-0, drawing level on sets.
Dolgopolov tried to resume focus by taking a break of serve in Tomic's first game in the third set but similar to the second, the two were very tight and the Australian once again took the set to a tie-break and snatched the round to go two sets to one up.
While it seemed that the number 13 seed had a mountain to climb, Tomic failed to keep his lead and the Ukrainian dominated the round, forcing the tie to a fifth and final set.
The deciding set started off by going the way of serve but Tomic was the first to find the breakthrough and clinched the winner.
The Australian will have to overcome Roger Federer to claim a place in the quarter-finals.