While he committed twice as many unforced errors as Rublev (22 to 11), fifth seed De Minaur still controlled most aspects of the match. Down 4-2 in the first-set tiebreaker, he ran off four straight points before winning his second set point. In the third set, he won 17 of 22 first-serve points and saved all three break points he faced.
The Australian will play sixth seed Grigor Dimitrov of Bulgaria in the semi-finals after Dimitrov outlasted Kazakhstan's Alexander Shevchenko 7-6, 3-6, 6-4.
Top-seeded Italian Jannik Sinner won his 200th career tour-level match when Canadian opponent Milos Raonic retired due to a right hip injury while down 7-6, 1-1. Sinner's opponent will be Dutchman Tallon Griekspoor, a 7-5, 7-6 victor over Finland's Emil Ruusuvuori.
IEB+ Argentina Open
In an all-Argentine quarter-final battle, Federico Coria upset fifth seed Sebastian Baez 6-1, 6-4 in Buenos Aires.
Coria served three aces without a double fault and converted five of nine break-point chances against Baez. His semi-final foe will be countryman and wildcard Facundo Diaz Acosta, who beat Serbia's Dusan Lajovic 6-4, 6-3.
The other semi-final will see top seed Carlos Alcaraz of Spain face third seed Nicolas Jarry of Chile. Alcaraz got past Italian qualifier Andrea Vavassori 7-6, 6-1, while Jarry advanced after sixth seed Tomas Martin Etcheverry of Argentina retired with the score at one set apiece.
Delray Beach Open
Second seed Frances Tiafoe eased into the semi-finals by beating Italian lucky loser Flavio Cobolli 6-4, 6-2 in Florida.
While Cobolli amassed a 7-4 edge in aces and saved seven of 11 break points, Tiafoe was too strong. He won not only 23 of 29 first-service points (79.3 per cent) but also 13 of 18 second-service points (72.2 per cent). Tiafoe set up an all-American semi-final showdown with third seed Tommy Paul, who beat Australia's Jordan Thompson 6-4, 6-3.
In Friday's two late matches, top seed Taylor Fritz defeated Australian Rinky Hijikata 6-3, 6-3, and Marcos Giron was a 6-4, 6-4 winner over wildcard Patrick Kypson.
