Nadal, 33, was sharp on serve as he raced into a two-set lead, allowing Carreno Busta just five return points.
Carreno Busta, seeded 27th, fared little better in the third as Nadal wrapped up a 6-1 6-2 6-4 win.
The 19-time Grand Slam champion could face Australian Nick Kyrgios in the last 16.
Kyrgios, 24, plays his third-round match against Russian 16th seed Karen Khachanov later on Saturday at Melbourne Park.
With Nadal and 23rd-seed Kyrgios not seeing eye-to-eye in recent years, the prospect of another meeting between the pair is a tantalising one.
Kyrgios cheekily mocked Nadal’s superstitious service routine, as did opponent Gilles Simon, in his second-round win over the Frenchman.
“It was my best match of the tournament without a doubt,” said Nadal, who hit 42 winners and made just seven unforced errors.
“When the conditions are warmer the ball bounces higher and flies through the air. That helps my game.
“I did very well with my serves and started to hit some forehands down the line. That is key for me.”
Nadal, who has only won the Australian Open once, in 2009, set up the potential blockbuster against Kyrgios with a clinical win over his friend Carreno Busta, with whom he helped Spain win the Davis Cup in November.
Nadal set the tone by breaking in the second game of the match, pinching Carreno Busta’s serve another four times on a sun-soaked Rod Laver Arena.
Victory also continued Nadal’s dominance over his compatriots. The Majorcan left-hander has now won his past 18 matches against Spanish opposition, stretching back to a 2016 Australian Open first-round defeat by Fernando Verdasco.