Top-seeded Nadal, who is eyeing to win 20th grand slam title and create record, conceded just five points on serve through his opening two sets, fired nine aces and zero double faults to register a 6-1, 6-2, 6-4 win over Busta.
"Had been my best match of the tournament so far, without a doubt, so that's a very positive thing. Sorry for Pablo who is a good friend of mine. I wish him all the best for the rest of the season," Nadal said after the match.
"I think today I did very well with my serve. And then I started to hit some very good forehands down the line, and that's the key shot for me," the 33-year-old added.
Nadal will now take on the winner between Nick Kyrgios and Karen Khachanov, who will meet each other later on Saturday.
However, it was the end of the roads for Karolina Pliskova in women's singles as she who went down to Anastasia Pavlyuchenkova in battle lasting for two hours and 25 minutes. Seed no. 2, the Czech player suffered a 7-6(4) 7-6(3) loss.
"I don't know what to say; I'm still in the match, still focusing on the next point.To beat Karolina for the first time, it's amazing," Pavlyuchenkova expressed after winning the match.
Pavlyuchenkova will now face No.17 seed Angelique Kerber.
Meanwhile, former World No.1 Simona Halep returned to the second week of the Australian Open for a third straight year, dispatching an in-form Yulia Putintseva, 6-1, 6-4 in her third round contest.
( With inputs from IANS )