The two-time champion at SW19 has seen his career beset by injury issues in recent years, with this his first appearance in the main draw since reaching the quarter-finals in 2017.
However, he won two matches at Queen’s Club ahead of the third grand slam of the season and treated the Centre Court crowd to a trip down memory lane on Monday, including a dramatic twist when seemingly on the brink of victory.
Having taken the first two sets, Murray somehow contrived to lose the third despite at one stage holding a 5-0 lead. The sudden collapse sent nerves jangling among the spectators as the roof was closed at the venue, but he responded impressively to the setback to triumph 6-4 6-3 5-7 6-3.
Speaking during his on-court interview after the triumph, the Scotsman once again reiterated he has no plans to make this year his Wimbledon swansong.
"It's been extremely tough. Even these last few months. It has been extremely frustrating not being able to get on the court," Murray said.
"I've had such little momentum over these last few years. I've kept trying, doing all the right things to be back in this position. I feel very lucky I get to do it again.
"I keep getting asked is this going to be my last Wimbledon. I don't know why I keep getting asked, though. No, I'm going to keep on playing.
"I want to play, I'm enjoying it. I can still play at the highest level. He is ranked 28th in the world and I beat him, so I will keep going."
Basilashvili saved two match points as he somehow survived in the third set by winning seven games in a row, though Murray responded to the setback impressively.
"I did well to win the fourth set in the end because that was mentally not easy going to the locker room after losing that third," Murray added.
Next up will be either Oscar Otte or Arthur Rinderknech, their contest having been locked at 9-9 in the deciding set when play on the opening day was suspended on the outside courts.