The 21-year-old Spaniard was characteristically relentless from the baseline on Monday as he ground down the No.27-ranked Khachanov's service games and converted four of 12 service break opportunities to win in 96 minutes.
"I always try to put some pressure when they're serving just to in a certain way tell them that I'm going to be there," Alcaraz said.
"If they want to win the service game or to beat me, they have to accept the battle and playing a really good tennis. For me, it's what I'm trying to show them all the time."
It was Alcaraz's 46th win of the season and the victory allowed the reigning French Open and Wimbledon champion to climb back above the absent Alexander Zverev into second place in the ATP live rankings.Â
Alcaraz will face Daniil Medvedev in the semis after the fifth-ranked Russian beat Flavio Cobolli of Italy 6-2 6-4.
Still seeking his first title of the year, Medvedev made 16 fewer unforced errors than the Italian and converted four of his eight break point opportunities as he closed out a solid 88-minute victory.
Earlier, Andrey Rublev beat Alejandro Davidovich Fokina 6-4 7-5 in a match carried over from Sunday because of a rain delay.
No.6-ranked Rublev had six aces and 21 winners to extend his career record against Davidovich Fokina to 5-0.
The fifth-seeded Russian was to play local favourite No. 96-ranked Bu Yunchaokete in the quarter-finals later on Monday.
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