The 27-year-old Scot, seeded 11th, triumphed with a 6-1 7-5 win in an hour and 25 minutes as he moved closer to qualifying for the season-ending ATP World Tour Finals in London.
After sailing through the first set, Murray started to struggle in the second, trailing 5-3 at one point to the Georgian qualifier before he struck back to record a win and set up a second-round meeting with Poland’s Jerzy Janowicz.
Murray said: “I started the match well and he wasn’t in very much of a rhythm at the beginning and I was dictating a lot of the points and using good variety.
“At the beginning of the second set I played a sloppy game on my serve and he gained some confidence from that and started playing better. He was timing the ball a lot better in the second set and I had to find a way to get through in the end.
“I was using a lot more high balls up to his backhand and that was pushing him back off the baseline and I was able to dictate the points. It was a good start....but there’s still work to be done.”
Murray moved up to ninth place in the race to reach the Finals when he followed up his tournament win in Shenzhen with a semi-final loss to Novak Djokovic in Beijing last week.