Murray took the first set 6-2 against Goffin in Thursday's quarterfinal showdown before the Belgian world No.45 called an early end to the match.
It will mark Murray's first semifinal in a top-tier ATP event since he won in Antwerp in October, 2019.
Murray's career appeared set for a limp end a few years ago when he was battling a serious hip injury that required two bouts of surgery and had him considering retirement.
But the 34-year-old, who is now ranked 135th, is feeling good and is aiming to produce a late-career purple patch.
Murray has won 46 titles on the ATP tour and he has set himself the goal of reaching 50.
The Sydney Tennis Classic could end up being title No.47 after an impressive run to the last four.
Murray couldn't help but feel for 31-year-old Goffin, who has been battling his own injury woes in recent times.
"He's missed the last eight months with injury. I believe he had surgery on the elbow, and he's had a problem with his knee for the last three or four months," Murray said during his on-court interview.
"It sucks. The injuries and stuff as you get older, they can get you down. Hopefully he's OK."
Murray needed more than three hours to dispose of Nikoloz Basilashvili a night earlier, but he found the going much easier against a wayward Goffin, who committed 19 unforced errors in the opening set.
Former world No.1 Murray converted two of his three break-point opportunities and he was happy with how he covered the court.
"The movement was what I was most pleased with," Murray said.
"I maybe made a few more errors than what I would have liked, but I felt I moved well, which was really positive.
"I finished after midnight yesterday and I did a lot of running, so it was good to come out and move well today.
"Hopefully do the same again tomorrow."