The win capped a fairytale run for the world number 76, who had already overcome two top-10 players in consecutive rounds in Felix Auger-Aliassime (world rank four) and Daniil Medvedev (world rank eight).
Both players battled blustery conditions but Majchrzak was the more aggressive player, taking more risks and eventually grinding down the obdurate de Minaur in a match lasting two hours and 25 minutes.
"This is a very emotional moment for me, I've been waiting for this moment all my career," said the 30-year-old as he collected his trophy.
"I played some of the best players in the world, so this one feels really good, it feels really special. To beat three players from the top 10 is an unbelievable run for me."
The Pole got off to a flying 3-0 start in the first set, breaking De Minaur's first service game as the Australian appeared to struggle with the swirling wind on serve.
That early break proved to be enough, as Majchrzak wrapped up the first set 6-3 with a high backhand volley at the net.
Losing his first set of the tournament appeared to galvanise the Australian, who broke Majchrzak's first service game of the second set with a crosscourt forehand pass.
But this time the Pole responded immediately, getting the set back on serve with a break of his own as De Minaur pushed a ground stroke long.
A series of unforced errors from Majchrzak at 3-2, however, gifted De Minaur another break of serve, and the Australian sealed the set 6-2 with another break as the Pole drifted a forehand drive wide.
The deciding set went on serve until the crucial seventh game, when Majchrzak seized the initiative, breaking the Australian's serve courtesy of a double fault.
But the stubborn de Minaur broke back immediately and won his next service game with a brilliant backhand pass up the line, one of the shots of the match.
A final-set tie-break seemed a fitting way to decide such a tight match.
De Minaur kicked off the breaker with a double-fault and Majchrzak gratefully accepted the gift to race into a 3-0 lead.
With a first title in his sight, the Pole tightened up somewhat, allowing the Australian to scrape back to 5-5, but a brave serve and volley gave him championship point.
In the end, De Minaur handed him the title with a double fault, Majchrzak sinking to his knees in triumph after the biggest win of his life.