The Serbian top seed, who has not lost before the last-eight stage at any tournament since Monte Carlo 10 months ago, must at least reach the semi-finals in the Emirates to stand a chance of stopping Daniil Medvedev from replacing him at the summit of the rankings.
Medvedev is competing in Acapulco this week and is guaranteed to end Djokovic’s world number one reign if he clinches the title.
There are other scenarios however that could allow Djokovic to extend his 361-week at at the top, should Medvedev falter in Mexico, but the Serb must at least make it to the final four in Dubai.
Djokovic followed up his opening round win over Lorenzo Musetti with a fifth victory in six meetings with Russian world number 26 Khachanov.
The five-time Dubai champion needed one hour 38 minutes to overcome Khachanov and set up a quarter-final against Czech qualifier Jiri Vesely, who knocked out Spanish eighth seed and last week’s Doha champion Roberto Bautista Agut.
“I thought the atmosphere tonight in the stadium was terrific,” Djokovic told a capacity crowd in Dubai that included his son Stefan and his former coach Boris Becker.
“It was equally good support for both Karen and me and for us as tennis players travelling around the world, this is what we play for, this kind of atmosphere, this kind of passion from the people that come to watch us, so I want to thank you from my heart.
“I missed it (competing) obviously, this is my life, this is what I’ve known to do and I still keep on doing for the last 20 years almost. Professional tennis is my love first of all. I enjoy travelling, I enjoy playing, I enjoy hopefully bringing some positive emotions and memories to people that come to watch.”
Djokovic went up a set and a break before Khachanov upped the pressure and struck back to level the second set at 4-4.
The Olympic silver medallist rallied the crowd behind him and swatted away a pair of break points to hang on to his serve but blinked in the tie-break to lose in straight sets.
Earlier on Centre Court, Jannik Sinner stopped Andy Murray from joining the 700 match-wins club as the Italian fourth seed advanced to the Dubai quarter-finals for a second consecutive year with a 7-5, 6-2 success over the former world number one.
Sinner had to save three match points in his opening win over Alejandro Davidovich Fokina but had a far simpler route to victory on Wednesday, facing zero break points against Murray in their one-hour 43-minute second round.
The 20-year-old Italian has improved his 2022 record to an impressive 9-1 and next takes on fifth seed Hubert Hurkacz.
“It’s a great start to the season, I’m just trying to play consistent, and now let’s see how the tournament goes,” said Sinner.
“It’s a very special feeling always (facing Murray), he’s a legend, winning three Grand Slams, many, many tournaments, he had so many unfortunate moments, many surgeries; his fighting spirit is incredible and obviously I wish him the best of luck.”
Second-seeded Andrey Rublev picked up a sixth consecutive victory with a battling 4-6, 6-0, 6-3 performance against South Korea’s Kwon Soon-woo to reach his third ATP quarter-final in as many weeks.
Rublev arrived late from Marseille, where he was crowned champion on Sunday, but has managed to quickly acclimatise to Dubai’s challenging outdoor conditions to book a last-eight clash with American Mackenzie McDonald.