Former World No 1 won the opening set 6-2 against the former world No 7 before Goffin pulled out of the match, just a game after receiving treatment to the back of his knee.
It is the first time that Murray has reached a tour-level semi-final since Antwerp in 2019. The Scot went on to win the title in Belgium three years ago, defeating former World No. 3 Stan Wawrinka in the final.
The wild card will now play American Reilly Opelka in the semi-finals following the fourth seed’s 7-6(4), 6-2 victory over countryman Brandon Nakashima in a 83-minute clash.
“It’s obviously been a while for me. I have been getting closer in the last few months, and my results would suggest that. So it’s good to get there this early in the season. Hopefully I can keep building from here and have a strong year,” said Murray.
“I want to try and win tournaments again. That’s one of the reasons why I’m still playing, because I believe I can still do that. I’m a couple of matches away from winning another one and I’ll give it my best effort to do that,” he added.
Meanwhile, top-seeded Russian Aslan Karatsev overcame Italy’s Lorenzo Sonego 6-2, 3-6, 6-2 to reach the semi-finals.
The World No 20, who was voted 2021 Most Improved Player of the Year, triumphed after two hours and 49 minutes in a hard-fought encounter.
Karatsev will now face Daniel Evans in the semis after the third seed edged American Maxime Cressy 6-4, 7-6(5) in one hour and 52 minute match. Evans won his first tour-level title in Australia last season at the Murray River Open in Melbourne.
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