Victory for the 32-year-old Nadal put him into the last 16 in New York for the 10th time and on course to add to his 2010, 2013 and 2017 titles.
However, 2009 champion and third seed Juan Martin del Potro, his potential semi-final opponent, also made the last 16 with a 7-5, 7-6 (8/6), 6-3 win over Fernando Verdasco.
Top seeded Nadal triumphed over Khachanov after an epic 4 hour 23 minute struggle on Arthur Ashe Stadium.
But the 22-year-old Russian had his chances.
He served for two sets to love lead in the 10th game of the second set and had set point in the fourth-set tiebreaker.
Nadal, seeking an 18th major, will face Georgia's world number 37 Nikoloz Basilashvili for a place in the quarter-finals.
The Georgian won just one game in a three-set loss to Nadal in their only previous meeting at Roland Garros last year.
Basilashvili reached the last-16 of a Slam for the first time by seeing off Argentina's Guido Pella 6-3, 6-4, 1-6, 7-6 (7/4).
"Karen played well. He's improving always. He's young. He has everything. I really see him winning a lot of matches in his career," said Nadal.
"For me personally, it was a physical, demanding match."
Khachanov, 22, and bidding to make the last 16 of a Slam for the third time this year, took the opener before Nadal needed strapping applied to support his right knee in the changeover.
"I am going to be at 100% for the next match," he assured reporters.
The top seed was quickly down 3-1 in the second set before battling back to 4-4.
Khachanov cracked when serving for a two sets lead in the 10th game.
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