The top-seed had lost the previous two finals to Jannik Sinner and Carlos Alcaraz, but he seized on the absence of the world's top two to make it third time lucky.
"It feels great to finally be able to lift the title," said the world number eight.
"Every day I got better, and I'm super pleased with the performance today," he added.
Canada's Auger-Aliassime threw everything at the 26-year-old, but the Australian soaked up the pressure and retrieved brilliantly to finally take the crown in Rotterdam.
The early games went with serve, but De Minaur seized the initiative in the 6th game, breaking the Canadian's serve with some trademark retrieving and a spectacular backhand winner up the line.
The top seed sealed the first set 6-3 with a powerful service, his consistency proving too much for Auger-Aliassime, who was left to rue 14 unforced errors, mainly on the forehand wing.
The pattern repeated in the second set, on serve until de Minaur clinched a break to love in the fifth game after two disastrous Auger-Aliassime double faults.
After this setback, the Canadian took a medical time-out for a reason that was not immediately clear, returning with no obvious movement issues.
However, de Minaur again broke his serve to love, Auger-Aliassime dumping a forehand into the net to put the Australian on the brink.
De Minaur made no mistake, taking the title with his first ace of the match and raising his arms in triumph and relief.
"Third time lucky. We finally managed to get the title," said the Australian as he collected the trophy.
"I'm glad I was finally able to get the title. It's been one of my favourite spots on the calendar. I love coming back here in Rotterdam. I've played some of my best tennis here, and I finally get the reward."
Auger-Aliassime paid tribute to his opponent, saying, "he had no holes in his games and I couldn't find a way."
"Sometimes I have to accept the loss and the fact that my opponent was better, and today he definitely was," added the Canadian.