Novak Djokovic and Carlos Alcaraz reach quarter-finals at Paris Masters
Serbia's former world number one, the sixth seed, beat the Russians 6-4 6-1.
The 21-time Grand Slam winner, 35, will face the third seed, Denmark's Casper Ruud, or Italy's Lorenzo Musetti, for a place in the semi-finals.
Earlier, world number one Carlos Alcaraz, 19, also reached the last eight with a straight-set win, beating Bulgaria's Grigor Dimitrov 6-1 6-3.
The Spaniard will face Russian seventh seed Andrey Rublev or Denmark's Holger Rune next.
Djokovic has won the title in his past two appearances, in 2019 and 2021, winning 16 of his past 17 matches in Paris - with his only loss coming against world number 19 Khachanov in 2018 final.
Although Djokovic broke Khachanov in his first service game, the Russian broke back to make it 3-3 before the Serb took his opportunity to clinch the set by breaking Khachanov again at 5-4.
Khachanov then held his serve, but Djokovic breezed through the rest of the second set to clinch victory in one hour and 27 minutes.
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