Kyrgios dominated the Spaniard, who will be confirmed as the new world number one when the rankings are released on Monday (August 21), on his way to clinching a 6-2, 7-5 triumph over the 15-time Grand Slam champion.

The Australian, known for his fiery behaviour on court, was among several players forced to play two matches on one day after adverse weather disrupted the schedule yesterday.

He had earlier overcome Croatia's Ivo Karlovic, while Nadal had booked a semi-final place with victory over compatriot Albert Ramos-Vinolas.

Kyrgios, the current world number 23, will take on David Ferrer in the last four after the Spaniard recorded an impressive 6-3, 6-3 victory over third seed Dominic Thiem of Austria.

The other semi-final will be between Bulgarian Grigor Dimitrov and American John Isner.

Dimitrov, the seventh seed, made light work of Yūichi Sugita as he swept aside the Japanese player 6-2, 6-1.

Big-serving Isner progressed by virtue of a 7-6, 7-5 win over compatriot Jared Donaldson.

In the women's draw, world number one Karolína Plíšková also won two matches as she booked her spot in the semi-finals.

The Czech tightened her grip on her current position at the top of the rankings by beating sixth seed Caroline Wozniacki of Denmark 6-2, 6-4.

"Whatever comes I will just take it," said Plíšková. 

"Even if I would be second coming to the US Open, it's still better than I was last year. 

"So no pressure about being world number one."

Plíšková will go up against Wimbledon champion Garbine Muguruza of Spain, who battled to a 6-2, 5-7, 7-5 success against Russian Svetlana Kuznetsova.

Romania's Simona Halep, the second seed, is also through as she dispatched Britain's Johanna Konta 6-4, 7-6.

American wildcard Sloane Stephens awaits for Halep in the last four as she progressed by beating Julia Görges of Germany 6-1, 7-6.