Britain’s top seed Cameron Norrie reached the Los Cabos Open final in Mexico after defeating Felix Auger-Aliassime 6-4, 3-6, 6-3.
Next time, defending champion Nuri will meet world number one Daniil Medvedev, who beat Serbian Miomir Kikmanovic.
It was Nouri’s first win over his Canadian opponent, who fired 17 aces to the British duo in the match.
In the quarter-finals of the Washington Open, there were defeats for the British pair Emma Radocano and Dan Evans.
“Felix has got me the last four times, so I really wanted to win this time,” Nouri said.
“The previous times I had match points, so I was thinking about that in the back of my mind. It was never easy.”
His next opponent, Russian Medvedev, is playing in his first tournament since June after 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 he will run into this month’s US Open – where he is the defending men’s singles title – confirming his world number one ranking.
Meanwhile in Washington, she defeated Russian Women’s Open defending champion Lyudmila Samsonova 7-6 (8-6) 6-1.
After a tight first set in which Samsonova saved four set points, the world number 60 overtook the English teenager in the second set.
Radocano, 19, was looking forward to reaching the semi-finals for the first time since winning the Grand Slam last year.
Samsonova will play China’s Wang Xiyu in the semi-finals after the 21-year-old defeated two-time Australian Open winner Victoria Azarenka.
And participates in the other semi-final match of Estonia Kaia Kanepi against Australian Daria Savile.
Meanwhile, Britain’s second-seeded Evans lost 7-6 (7-5) 4-6 7-5 to Japan’s Yoshihito Nishioka in the quarter-finals.
It was the two’s fifth meeting – Nishioka won all five matches.
Top seed Nishioka will face Andrey Rublev in the semi-finals. Russian Rublev played twice on Friday in a crowded slate of games due to late rain, but beat Americans Maxime Cressi and JJ Wolff.
Australian Wimbledon runner-up Nick Kyrgios plays Sweden’s Mikael Ymir in the other semi-final match.