Dimitrov fought back from one set down to take it to a deciding third before Nadal proved to be too strong as he converted his second match point to seal the victory.
Earlier, second-seeded Simona Halep reached the semifinals by beating Daria Kasatkina 6-2, 6-1.
Victor edges Halep closer to taking the world number one ranking held by Spain's Garbiñe Muguruza, who bowed out of the tournament in the first round with a virus.
"He has a massive future ahead and I'm really good friends with him so it's always fun playing him". I don't know how many I had. It's going to be a big one and big test for me. Both players excel with their playing styles and their world-class tennis was what allowed them to enter the world's top 10, especially for Nadal and his 16 Grand Slam titles.
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Ukraine's Elina Svitolina, who has already qualified, beat Russian Elena Vesnina 6-2, 7-5 to also enter the quarter-finals.
She will meet the victor of the quarter-final between Ukrainian third seed Elina Svitolina and unseeded Frenchwoman Caroline Garcia.
Halep will play the victor of the semifinal between Garcia and 12th-seeded Petra Kvitova of the Czech Republic.
Goffin, chasing his second consecutive title after winning in Shenzhen last week, saw off Richard Gasquet 7-5 6-2 and Schwartzman was a 6-0 7-5 victor over Steve Johnson.
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Ostapenko entered the semifinal without the loss of a set during the week.
Nadal will next face John Isner. She cemented her lead with another break in the seventh game for a 5-2 lead to serve out the set.
Zverev, 20, served two crucial double faults at 5-5 in the final set, handing Krygios the break, before the world number 19 dispatched his final service game in style. At 40-0 in the final game, Halep won with a clean forehand victor down the line.
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Kuldeep Yadav, the left-arm wristspinner, made for a study in contrast with his lengths in the first half of his spell. But it was the batting that led them down, especially the collapse that we have seen so often after Finch's wicket.