The Australian Open champion fought off a match-point to beat Vladimir Voltchkov and book his spot in the semi-finals of the San Jose Open.
The Spanish ace will meet Argentina's Mariano Puerta in Sunday's title round for the French Open men's singles crown.
Andy Murray's hopes of a first Grand Slam quarter-final ended in disappointment when he was beaten 6-1, 5-7, 6-3, 6-0 by seventh seed Nikolay Davydenko of Russia.\n\n
A double fault earned the Russian his eighth ATP title after two hours and seven minutes.
Rohan Bopanna and his Pakistani partner Aisam-Ul-Haq Qureshi continued their fine form and advanced to the men's doubles quarter-finals of the Dubai Duty Free Championships.
Nadal, is known to have a superior win-loss record over most top players (including Andy Murray and Novak Djokovic), but believe it or not, there are players on the circuit who have an edge over Nadal.
Medvedev became only the fourth player in ATP history to beat the world's top three at the same tournament.
Indian tennis players enjoyed an all-win day at the US Open as three of them reached the men's doubles third round with their respective partners, while Sania Mirza entered the women's doubles pre-quarters.
It was end of US Open campaign for Somdev Devvarman and Mahesh Bhupathi after they lost their respective hard-fought matches even as Rohan Bopanna had a mixed day.
Daniil Medvedev continued his march towards a first Grand Slam title on Wednesday, powering into the US Open semi-finals with a clinical 7-6(6), 6-3, 7-6(5) victory over childhood friend Andrey Rublev.
The winners of the season's first three grand slams Novak Djokovic, Andy Murray and Rafa Nadal put on a masterclass at the Western and Southern Open on Wednesday, strolling into the third round with straight sets wins.