The Mallorcan, seeking to claim a record 21st Grand Slam title in the absence of great rivals Roger Federer and Novak Djokovic, was sensational as he took a two-set lead.
But Khachanov, seeded 28th, threw caution to the wind in the third set, stalling Nadal's charge with some ferocious hitting.
Olympic runner-up Khachanov had lost all seven previous meetings with 2009 Australian Open champion Nadal but briefly looked capable of mounting a comeback.
Nadal seized back control with a break of serve at the start of the fourth and with the clock having ticked past midnight he finished off the match in a hurry.
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