Machac, a top 20 player last year, was fizzing winners onto the lines and Australia's No.1 seemed to have no answer to his excellence.
The Czech was six points from victory and de Minaur's chances of making the end-of-season ATP Finals were receding rapidly as a first round exit loomed in the Austrian capital.
But Demon never quits. He won the next four points to hold, then broke Machac in a three-deuce game. He then survived a break point on his next service game, which lasted nearly nine minutes, then broke again to take the set.
Machac broke immediately in the third set but it was a last hurrah. De Minaur took the next five games before completing a near-two-hour 1-6 6-4 6-3 win with an ace.
De Minaur greeted Monday's victory with a roar of delight, relief and vindication. The 27-year-old has made a career out of comebacks but few have been such a turnaround as this.
"For three-quarters of that match it was very tough for me," he said. "I have dug deep, found a way to get a crucial break when I needed it, and the momentum changed."
Referring to his recent run to the final in Beijing, and a narrow quarter-final loss to Alexander Zverev in Shanghai, he added: "The last couple of tournaments I've learned a lot about myself and was able to draw on those situations and come out with some big serves when I needed it."
The world No.10 had come back to win after losing the first set in his only previous match with Machac, in Monte Carlo last year. But on that occasion he lost the first set 6-3, then roared back to win the second 6-0.
This was much more of a precipice. He had lost the first set 6-1 in 34 torrid minutes having landed only a third of his first serves to Machac's three-quarters.
De Minaur began Vienna's ATP 500 event tenth in the standings for the season's Turin finale and, with Jannik Sinner's competitive season over, needs to be in the top nine to qualify.
Sinner, incidentally, is set to make his comeback in the lucrative Six Kings Slam in Riyadh, Saudi Arabia, according to organisers of an event postponed to late December after an attack by Yemen's Iran-aligned Houthis on Riyadh's international airport killed 13 people.
Sinner is the winner of the previous two Six Kings, earning $US6m ($A8.5m) each time. A non-ATP event it was originally due to take place in October.
De Minaur is also playing in the event, as are Carlos Alcaraz, Novak Djokovic, Alexander Zverev and Taylor Fritz.
Back in Vienna, where Jakub Mensik, Arthur Fery and Matteo Barrettini also won, De Minaur will next meet American world No.18 Learner Tien or France's Luca van Assche in the last-16.
Meanwhile, in Basle, Switzerland, Rinky Hijikata could do de Minaur a favour.
Qualifying in the ATP 500 as a lucky loser he will meet American Fritz, currently 12th in the Race to Turin standings, on Tuesday.
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