The Spanish top seed came through a riveting clash on Rod Laver Arena 6-3, 3-6, 7-6 (8/6), 7-6 (7/4) to end the gallant hopes of the basketball-mad Australian, who came on court wearing an LA Lakers shirt in honor of Kobe Bryant, AFP reported.
He will now face fifth seed Thiem after the Austrian swept past Gael Monfils 6-2, 6-4, 6-4.
"What can I say about Nick? When he is playing like today with this positive attitude he gives a lot of positive things to our sport," said Nadal, the 2009 champion who is looking to match Roger Federer's record 20 Slam crowns.
"He's one of the highest talents we have on our tour and I like the Nick Kyrgios during the whole of this tournament."
"I just feel happy that I won one more match tonight, an important one," he added.
It was billed as a grudge match after a series of bad-tempered exchanges last year when Nadal accused Kyrgios of lacking respect and the Australian fired back that the Spaniard was "super salty."
But Kyrgios struck a conciliatory tone beforehand, calling Nadal "a hell of a player", and it was played with respect from both sides.
Germany's Alexander Zverev ended the hot streak of his close friend Andrey Rublev of Russia to reach the Australian Open quarterfinals for the first time on Monday.
The seventh seed broke once in each set for a clinical 6-4, 6-4, 6-4 win in just 1hr 37mins to go into a match-up with Stan Wawrinka, the powerful Swiss who beat Russia's Daniil Medvedev.
Zverev retains his 100 percent record over Rublev, who came into the match on a 15-match winning run including titles in Doha and Adelaide earlier this month.
After a long embrace at the net, Zverev, 22, said, "I've known him since we were 10 years old. I just reminded him how far we got together.
"A lot of young kids would dream about playing the fourth round of a Grand Slam against one of his closest friends. I just told him we're going to play a lot of great matches."
It was a one-sided win for Zverev, who faced no break points as he reached his first quarterfinal in five visits to Melbourne – equaling his best Grand Slam result, achieved last year at Roland Garros.