The world number 53's previous high point of the campaign was his advance to the fourth round of the French Open but his victory over third-ranked Murray marks the fourth time the 30-year-old has secured a win against a top-10 opponent.
"I was exhausted at the end because my body was really tired but I learnt to play good points and I learnt to play aggressive and without any fear because you have to fight for every point," Gabashvili told reporters.
Gabashvili reached the third round of the U.S. Open a year ago and his liking for the hard courts of North America was evident in the first set when he took the contest to Murray and broke the Scot twice to claim the opener.
Attempting to make the transition from grass to hard courts, the top seed appeared to shake off the rust in the second set to level the match but was unable to seal the deal when he was broken as he served for the contest at 5-4 in the decider.
"It's obviously a disappointing match to lose but it wasn't like I was blown off the court in a match that I had no chance of winning. I feel like I put myself in a position to win the match," Murray said.
"It was the first hard-court match for four-and-a-half months with only four or five days of preparation, so I was happy with how I moved and did certain things on court.
"But there are some things for me to improve and hopefully with a few more days and having that match under my belt, I'll be able to make some improvements for the next few weeks."
Murray, who was awarded a first round bye, fell to Roger Federer in the Wimbledon semi-finals last month but had since helped Great Britain advance to the last four of the Davis Cup for the first time since 1981.
The U.S. Open starts on Aug. 31 in New York where Croatia's Marin Cilic will defend his title.
(Writing by Jahmal Corner; Editing by John O'Brien)
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