The Aussie No.1 lost the first three games en route to dropping the first set and though he drew back to level with a much better second set that proved illusory.
The big-hitting Croatian veteran prevailed to win 6-2 3-6 6-3 in two hours 17 minutes to set up a last-16 match on Wednesday (2100 AEDT) with Australian No.2 Alexei Popyrin.
There was Aussie joy, however, for Chris O'Connell, albeit in unsatisfactory circumstances. The qualifier moved into the second round after his opponent, world No.16 Grigor Dimitrov, retired through injury after losing the first set 6-0 in 24 minutes.
O'Connell will now meet former Wimbledon finalist Matteo Berrettini, who beat Novak Djokovic last week, in the early hours of Thursday morning AEDT. The Italian beat Gael Monfils 7-5 6-4 on Tuesday.
Cilic, 36, had not won a Tour-level match in 2025 nor beaten a top-ten player in 21 months. But he found form with 21 winners to de Minaur's nine.
"Winning the first three games, getting a feel for the court, the conditions, was a great start for me," said Cilic, the world No.3 seven years ago but now placed 187th.
"It was a little gusty, but I was feeling the ball extremely well. I know how dangerous Alex is. He is an incredible runner on the court, he gets some balls that nobody gets. I had to stay patient but aggressive. I'm just so pleased that I was able to keep that great level throughout the whole match."
De Minaur, who was the No.2 seed, forced two break points in the decisive set, but could not take either. He found the windy conditions treacherous, making 32 unforced errors.
Popyrin has not played Cilic for nearly three years, the pair having one win apiece in their two previous meetings.
De Minaur's was not the only surprising exit.
French qualifier Quentin Halys beat last week's Doha winner Andrey Rublev, the world No.9, 3-6 6-4 7-6 (7-5).
Halys, 28, ranked 77, saved five break points at 5-5 in the final set before emerging victorious in two hours, 12 minutes.
"What a victory," he said. "I played really well today. At the beginning I was a bit nervous, but at the end I was pretty calm. The key was to serve well, be aggressive and make amazing shots."
Nuno Borges also overcame a higher-ranked player, thrashing world No.19 Arthur Fils 6-2 6-1.
Top seed Daniil Medvedev avoided the shocks, defeating Jan-Lennard Struff 6-4 7-6 (7-4). Ugo Humbert and Felix Auger-Aliassime were among other winners.
