The Spaniard produced some stunning tennis and made the 19-year-old work for every point as he continued his campaign for a second Melbourne title.
The Australian had the backing of the Rod Laver Arena and showed his enormous potential early on as he went toe-to-toe with the 17-time Grand Slam champion.
However, De Minaur just could not live with Nadal's power and consistency, and he fell to a straight-sets defeat in two hours, 22 minutes.
Nadal will now face Tomas Berdych in the last 16:
De Minaur did not play poorly, yet as the scoreline suggests, he was almost completely dominated by Nadal.
The opening exchanges were phenomenal from both players. In the second game of the match, the Aussie showed impressive energy and steel as he saved four break points to hold for 1-1.
The youngster then took advantage of back-to-back double faults from Nadal, 32, to earn two break points, but inevitably the Spaniard hauled the game back to deuce.
A huge forehand winner gave De Minaur another opportunity, but Nadal went to the net to save the third break point and duly held for a 2-1 lead.
The first three games of the match took 23 minutes, and it looked as though De Minaur could put on a show on Rod Laver.
He could not maintain the intensity with which he had opened the match, though, and consecutive breaks from Nadal saw him take the opening set 6-1.
It was vital De Minaur got back on the board with a hold in the opening game of the second set, but there was no let-up from Nadal.
In a 15-minute game, the teenager saved four more break points and must have thought he had finally held when he hit deep and approached the net with the advantage.
A ludicrous forehand pass from Nadal kept him in the game, though, and he won his sixth game in a row when De Minaur went long on the fifth break point.
In his next service game, the No. 27 seed finally got an easy hold for his first game in eight.
However, at a set and a break down, it was a long way back for the youngster. He needed Nadal to give him a glimpse of an opportunity, but when any door opened up, the Spaniard slammed it shut.
At break-point down serving for the second set, Nadal pummelled an inside-out forehand into the corner and went 2-0 ahead.
After again being broken in the opening game of the third set, De Minaur carved out half a chance to break back for 1-1 as he took a 0-30 lead.
He returned deep into the corner two points later and looked to have guaranteed himself two break points. But an off-balance Nadal somehow managed a near-impossible backhand passing winner and held for 2-0 in the third.
It was a morale-sapping blow for De Minaur. He gamely kept going, producing some moments of magic for the home support to savour.
Nadal never wavered, though, and his level never dropped. As well as De Minaur played, he could find no way to stop the Spaniard wrapping up victory.