The Spaniard tamed the big-serving American John Isner 6-4, 7-6 (0) yesterday to set up the clash with the third-seeded Bulgarian.
"He played so aggressive, having a lot of success, hitting a lot of winners, returning very well".
"Everybody knows that he serves huge and it is so hard to break him".
The US Open champion lost to Isner at the Laver Cup last month but looked sharp, playing a brilliant second-set tie-break to win 6-4 7-6 (7-0).
But he was always in control against Khachanov, 21, breaking him in the fourth game of the first set on the way to a routine victory.
On the women's side, unseeded Carolina Garcia of France upset third-seeded Elina Svitolina of Ukraine 6-7 (5), 7-5, 7-6 (6) in nearly 3 1/2 hours to line up Petra Kvitova in the semifinals.
The loss was a big blow to Berdych's campaign to make it to the Nitto ATP Finals. Cirstea will next take on Latvia's Jelena Ostapenko, the reigning French Open champion, who enjoyed a good start and stormed to a 3-0 lead before Peng calling for the timeout to deal with her knee injury.
Last year's match saw Dimitrov break the Nadal serve five times and he spoke of his delight with the triumph: "I'm pretty happy with that win, " Dimitrov said.
To bump Garbine Muguruza from No. 1, the Romanian needs to reach the final.
In the women's singles event, second-seed Simona Halep also made it to the semi-finals after clinching an easy 6-2, 6-1 win over Daria Kasatkina of Russian Federation in their last-eight clash.
Garcia is in red-hot form after winning the Wuhan Open Saturday.
She is now in 10th place and winning the China Open will help her overtake eighth-placed Briton Johanna Konta, going into the penultimate week of the season.
In the women's event, world number two Simona Halep of Romania is through to the semi-finals with a 6-2, 6-1 win over unseeded Russian Daria Kasatkina.
Nadal has had an incredible season thus far, reaching three Major finals and extending his Grand Slam haul to 16, while Dimitrov reentered the top-10 with some consistent results which allowed him to reclaim his status of being a contender at the major tournaments.
'Glee' star pleads guilty to child pornography charges
Salling would have potentially faced up to twenty years behind bars had he gone through with the trial and was found guilty. Salling played bad-boy football player Noah "Puck" Puckerman on the hit U.S. show Glee from 2009 to 2015.