The Scot battled to a five-set victory over the big-hitting Georgian, who he also defeated on his way to his first ATP final in three years at the Sydney Classic last week, but was left annoyed by repeated shouts from the stands, apparently imitating Cristiano Ronaldo's 'Siuuu' celebration.
He said: "There were some people booing during my practice yesterday. I have no idea what for. So originally that's what I thought it was. It was incredibly irritating."
Murray focused on the future not the past after returning to the court where he was virtually retired three years ago.
The great and the good of tennis were hastily gathered together to make a tribute video for Murray in 2019 after he tearfully laid bare the extent of his hip problems on the eve of the tournament and announced he was considering retiring.
But, even as the video was playing, Murray, who had somehow defied the pain to push Roberto Bautista Agut to five sets in a raucous atmosphere, was looking ahead to his imminent resurfacing operation and the hope that he might be able to come back.
Comparisons were inescapable as he again found himself in a five-set battle, this time with 21st seed Nikoloz Basilashvili, but optimism has been growing that Murray can write a very different ending to his story and he battled to a 6-1 3-6 6-4 6-7 (5) 6-4 victory.
Asked whether it had brought back memories, Murray said: "I would like to say that there was loads, but that wasn't the case. I practised on it a couple of times when I arrived in Australia. And it felt like it always felt on that court.
"I've put in a lot of work to get back here. I have played on this court many times and the atmosphere is incredible. I have always had fantastic support.
"This is where I thought I had potentially played my last match three years ago but it is amazing to be back, winning a five-set battle like that. I could not ask for any more."
Murray, for whom this was a first victory in Melbourne in five years, went into the match on the back of a run to his first ATP Tour final for more than two years, with his scalps including big-hitting Georgian Basilashvili in a three-hour tussle.
Melbourne Park's third court has been the scene of many Murray scraps over the years.
Initially this looked like it might not be one as Basilashvili struggled to find the court and Murray, with little effort required, raced to the first set in a little over 20 minutes.
Basilashvili, who Murray also defeated at Wimbledon last year despite a dramatic third-set collapse, mis-hit one serve so badly that it flew high into the stands without bouncing.
But Basilashvili is a man entirely committed to the game plan of hitting the ball as hard as possible at every opportunity and swings from the sublime to the ridiculous are par for the course.
The third set was a one-act melodrama featuring searing winners, errant smashes, wild errors and an awful lot of Murray scampering around well behind the baseline trying to force Basilashvili to self-destruct.
The fourth followed a similar pattern, although this time with Basilashvili winning, but, although the Georgian clawed his way back from 1-4 in the decider to level, it was Murray who made it across the line.
Murray next takes on Japanese qualifier Taro Daniel, and he added: "I will hopefully keep improving. There are things in my game I can definitely do better.
"I would love to have a deep run here, if possible. It is something I have not had in one of the slams since I came back from injury and it is something that is motivating me.
"I have played some of my best tennis here over the years. I feel comfortable here and I hope I can do it here this tournament."