Britain’s top seed Cameron Norrie reached the final of the Los Cabos Open in Mexico after defeating Felix Auger-Aliassime 6-4, 3-6, 6-3.
The defending champion Nuri will then meet world number one Daniil Medvedev, who beat Serbian Miomir Kikmanovic.
Nouri’s first win was over his Canadian opponent, who fired 17 aces against two Britons in the match.
The quarter-finals of the Washington Open saw defeats for British couple Emma Raducano and Dan Evans.
“Felix caught me the last four times, so I really wanted to win this time,” Nouri said.
“I used to get matching points, so I thought about it in the back of my mind. It’s never easy.”
His upcoming opponent, Russia’s Medvedev, is playing in his first tournament since June after recovering from injury – and Ban on Russian players at Wimbledon.
But it will be his fourth final this year, after beating Kikmanovic 7-6 (7-0), 6-1.
This means that he will enter this month’s US Open – where he is the defending men’s singles title – with an assurance of the world rankings.
Meanwhile in Washington, she defeated Russian Open champion Lyudmila Samsonova 7:6 (8:6) and 6:1.
After a tight first set in which Samsonova saved four set points, the world number 60 overtook the young Englishman in the second set.
Radocano, 19, was aiming to reach the semi-finals for the first time since winning the Grand Slam last year.
Samsonova will face China’s Wang Xiyu in the semi-finals after the 21-year-old defeated twice Australian Open champion Victoria Azarenka.
In the other semi-final match, Estonian Kaia Kanepi will meet Australia’s Daria Savile.
Meanwhile, Britain’s second man, Evans, lost in the quarter-finals to Japan’s Yoshihito Nishioka 7:6 (7:5), 4:6, 7:5.
This was the fifth meeting between the two – and Nishioka won all five matches.
Nishioka will meet top seed Andrey Rublev in the semi-finals. Russia’s Rublev played twice on Friday in a packed schedule due to rain delays, but defeated Americans Maxime Creasy and JJ Wolff.
Australian Wimbledon runner-up Nick Kyrgios plays Sweden’s Mikael Ymir in the other semi-final match.