The three-time champion started late on a windy night on Court 1, but negotiated the conditions well as he set up a meeting with Kei Nishikori in the last-eight with a 6-4 6-2 6-2 win.
In doing so, the 12-time major winner moved level with Jimmy Connors in second place on the list of the most quarter-final appearances in Grand Slam finals, while moving level with Andy Murray on 10 quarter-final showings at the All England Club.
Djokovic (41) now sits behind only Roger Federer (53) in terms of Grand Slam quarter-final appearances, while he and Murray sit behind Federer, Connors and Boris Becker at Wimbledon.
Most Wimbledon quarter-final appearances
16 – Federer
14 – Connors
11 – Becker
10 – Djokovic
10 – Murray
9 – McEnroe
9 – Sampras
Most Grand Slam quarter-final appearances
53 – Federer
41 – Connors
41 – Djokovic
36 – Agasi
35 – Nadal
34 – Lendl
Federer had earlier extended his leads at the top of both lists with a 6-0 7-5 6-4 win over Adrian Mannarino, while Nadal moved to fourth on the all-time list of Grand Slam quarter-finals by defeating Jiri Vesely 6-3 6-3 6-4.
There had been some controversy in the build-up to Djokovics match over scheduling.
Before Kevin Andersons tie with Gael Monfils had concluded on Court 1, Jamie Murray and Victoria Azarenkas mixed doubles match was switched to Centre Court – leaving many fearful that Djokovic would not be able to complete his match.
It harked back to last years scheduling fiasco, where Wimbledon chiefs refused to move the Serbs last-16 encounter with Adrian Mannarino to Centre and ultimately forcing him to play back-to-back matches on Tuesday and Wednesday, with Djokovic then withdrawing from the tournament with an elbow issue.
However, Anderson wrapped up the fourth set soon after and Djokovic made light work of Khachanov to beat the light and book his spot among the final eight.
His next opponent will be Japans Nishikori, who will contest the quarter-finals for the first time here at Wimbledon.
The former US Open finalist recovered from a set down to beat Ernests Gulbis and awaits Djokovic on Wednesday.