In a match of high quality and tension, 19-year-old Tomic sank the 13th seed 4-6 7-6 (7-0) 7-6 (8-6) 2-6 6-3 in three hours and 49 minutes.
One of only two Australians left in the singles draw, Tomic will now take on Roger Federer in the fourth round on Sunday.
But after Dolgopolov squared the match at two sets all, Tomic benefitted greatly from an umpiring call in the opening game of the fifth set, in which he clearly appeared to challenge a call mid-point.
His raised racquet and eyebrow went unnoticed, he won the point and the game, leaving Dolgopolov fuming and playing catch-up for the rest of the set.
Tomic later broke the Ukrainian to go 3-1 up, and never relinquished his advantage to ensure his best-ever finish at an Australian Open regardless of how he performs against Federer.
“I looked at the ref, but I didn’t say a thing, I continued to play,” Tomic said. “In my mind, I didn’t challenge.”
In a tactical match in which the players swapped slices as often as clear winners, Tomic fought back from losing the first set – and kept fans biting fingernails from that moment on.
The teenager was taken to a tie-break in the second set, but clicked up a gear to win it to love.
Then the Ukrainian took an early service break in the third set, before Tomic broke back and forced another tie-break – this a far more tense affair then the second set.
Trailing 5-3 in the breaker, Tomic again found what he needed to fight back and win.
But Dolgopolov then grabbed an early fourth set break of serve, before a six-minute medical timeout to attend to a back problem.
The rub-down on his back appeared to release a genie within – Dolgopolov winning the next three games to close out the set, before the early fifth set controversy swung the momentum Tomic’s way.
As glamorous girlfriend Donay Meijer watched, Tomic put his nose in front when he broke Dolgopolov in the fourth game of the deciding set.
Tomic believed the electric atmosphere on Rod Laver Arena helped him close out the match.
“I think the crowd made me win,” Tomic said. “He’s one of the most unusual guys to play. For me to play him in this round and win is fantastic for me.”
Tomic and Lleyton Hewitt, who is scheduled to play his third round match on Saturday against Canadian Milos Raonic, are the only Australians left in the singles tournaments.