The 18-year-old was cheered off by the home crowd at the Pat Rafter Arena.
De Minaur said he was, 'lost for words,' after the victory, and said he had played an, 'unbelievable match.'
Sealed with an ace - Kyrgios takes Brisbane title in impressive fashion
He will face Michael Mmoh in the quarterfinals after the American defeated Argentina's Federico Delbonis.
Nick Kyrgios overcame a knee scare to progress to the quarter-finals of the Brisbane International.
The Australian, who was making his first appearance on the circuit since October following shoulder, hip and knee injuries, called a medical timeout towards the conclusion of the first set.
But Kyrgios, 22, despite dropping the opener, recovered to win 6-7 (3/7) 7-6 (7/5) 6-2.
Kyrgios produces sublime fake out winner
Additional reporting from PA.
Kyrgios gets Brisbane title boost ahead of Australian Open