The victory extended Nadal’s 17-match winning streak over Spanish players, having not been beaten by a fellow countryman since losing to Fernando Verdasco at Melbourne Park in 2016, Reuters reported.
“It was my best match of the tournament so far, without a doubt,” Nadal told reporters.
“I have been serving well, starting to create damage with the forehand. Hitting serve on one shot, I think.”
Nadal, bidding for a record-equaling 20th Grand Slam trophy, claimed victory when Carreno Busta sent a backhand into the net, setting up a meeting with Australian Nick Kyrgios.
Firebrand Kyrgios scraped past Karen Khachanov on Saturday in five thrilling sets to set up a grudge match against Nadal.
The Australian showman came through a tense battle with the Russian 16th seed after 4hrs 26 mins in front of passionate home support on Melbourne Arena to win 6-2, 7-6 (7/5), 6-7 (6/8), 6-7 (7/9), 7-6 (10/8), AFP reported.
"Mate, it was crazy, I don't even know what to say right now, it was insane, I have no words for how I'm feeling right now," said Kyrgios.
Kyrgios tried to play down the feud with Nadal, saying, "He has a winning record against me. Whatever happens between us, he's an amazing player, he's arguably the greatest of all time."
Asked about 23rd seed Kyrgios after his match, Nadal was also diplomatic.
"When he plays good tennis and he shows passion for this game, he is a positive player for our tour.
"When he's doing the other stuff, of course I don't like."
Fifth seed Dominic Thiem will face Gael Monfils in the fourth round after beating Taylor Fritz 6-2, 6-4, 6-7 (5/7), 6-4.
The 26-year-old broke the American on three occasions to take a 2-0 lead before the 29th seed edged his Austrian opponent in the third-set tie-break.
Thiem secured victory in the 10th game of a tight fourth set when he broke his opponent to love.
Earlier, Monfils beat Latvian qualifier Ernests Gulbis 7-6 (7-2) 6-4 6-3.
Stan Wawrinka, who won the title in 2014, moved into the fourth round when big-serving John Isner retired from their match with an apparent foot injury.
Swiss Wawrinka led 6-4, 4-1 when the American pulled out.
Russian 17th seed Andrey Rublev recorded his 15th consecutive victory with a 2-6 7-6 (7-3) 6-4 7-6 (7-4) win over Belgian 11th seed David Goffin.
Rublev, who has won titles in Adelaide and Qatar this year, will now play German seventh seed Alexander Zverev in round four.
Zverev has yet to drop a set in the tournament after registering a 6-2, 6-2, 6-4 win over Spain's Fernando Verdasco.
World number four Daniil Medvedev eased past Alexei Popyrin in straight sets to set up a last-16 clash with Wawrinka.
The tall Russian had few problems dispatching the unseeded Australian 6-4, 6-3, 6-2 on Rod Laver Arena as he steps up his quest for a maiden Grand Slam crown.
"I knew it was not going to be easy and happy to win in straight sets," said Medvedev, insisting he had no expectations in Melbourne.
"(But) of course every time no matter what tournament I'm super disappointed (if I lose).
"Hopefully I can win seven matches here, but very tough."
He now plays experienced 2014 champion Wawrinka after the Swiss got an easy ride through his clash against John Isner, with the American retiring injured while losing 6-4, 6-1.
Elsewhere, Simona Halep put away Kazakhstan's Yulia Putintseva 6-1, 6-4 to reach the last 16, where she will play Belgium's Elise Mertens, who won in three sets against CiCi Bellis – ending the American's Grand Slam return from long-term injury.
Halep, the reigning Wimbledon champion, shrugged off the departure of some of the tournament favorites, saying defeats can happen to anyone.
"It's just a tournament, and I'm sure that for you guys (media) it's a little bit of shock when the top-10 players are losing, but it's life and we cannot be 100 percent every day," said the Romanian.