Djokovic must at least reach the semi-finals in Dubai 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 stay 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.
The Serb later weighed in on Zverev's violent behaviour towards a chair umpire that got him kicked out of the ATP event in Acapulco.
Djokovic, who was disqualified from the US Open in 2020 for accidentally hitting a line judge with a ball, said he expects 24-year-old Zverev to reflect on what he has done.
"I think he said it all in that statement. He realises that it was a mistake. I understand the frustration. Sometimes on the court, you feel in the heat of the battle lots of different emotions," said Djokovic.
"I made mistakes in the past where I've had tantrums on the court. I understand what the player is going through. But, of course, I do not justify his actions. He has, with the words that he had in the statement, handled it in a right way."
The ATP has yet to reveal the extent of the fine Zverev will no doubt be handed, and it is unclear whether a suspension is on the table.
Djokovic firmly stated he would never encourage the tour to hand out harsh sanctions against a player and said there were many others who have committed similar offences.
"I'm never going to encourage ATP disqualifying or fining a player because I'm not in a position to do that. Why would I do that?," said the 20-time major winner.
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