The Serb committed just a dozen unforced errors on Monday and hit 29 winners to dispatch Khachanov as night fell on the All England Club, reports Efe.
Next up for Djokovic, the tournament's 12th seed, will be Kei Nishikori of Japan who defeated Ernests Gulbis 4-6, 7-6 (5), 7-6, (10), 6-1 in a gruelling contest that went on for three hours and 28 minutes.
"I'm very pleased," Djokovic said after the victory.
"He started off with a break. He made a couple of great shots but I managed to break and get back into the set. He's got weapons, a big first serve and a big forehand, but I managed to get serves back and make him play another shot," he added.
With a 10th appearance in the Wimbledon quarterfinals, Djokovic moves into a tie with Andy Murray behind Roger Federer (16), Jimmy Connors (14) and Boris Becker (11).
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