The match had to be suspended at 6-6 in the first set after the heavens opened and doused centre court.
Once the Qizhong Tennis Centre roof had been closed and a host of volunteers had towelled and blowdried the court, world number 19 Dimitrov inched a tight tiebreaker and followed that by taking the second set.
"I knew it was going to be a very competitive match... (Khachanov's) hungry and he's so competitive -– but so am I," said the 32-year-old Bulgarian after his win.
"The rain was not pleasant but in the end you need to adapt and that's what I was able to do."
Top seed Carlos Alcaraz is looking to book his own place in the fourth round later against Britain's Daniel Evans, ranked 33rd in the world.
Already through is Jannik Sinner, who knocked Alcaraz out of the China Open semi-finals in Beijing last week.
But defending champion Daniil Medvedev is out of the tournament after a shock defeat at the hands of 26th-ranked American Sebastian Korda on Sunday.
© 2023 AFP