It was a repeat meeting of the Davis Cup from last year, which Murray won to seal the trophy for Great Britain, and even though the Scot this time finished the job in two sets he was made to work very hard.
World No 13 Goffin produced a good comeback in the second set and briefly threatened to take the match to a decider, but second seed Murray was able to hold on and book a meeting with France’s Lucas Pouille.
Murray, who parted company with coach Mauresmo this week, is yet to drop a set in this tournament so far and victory on Friday makes it a third-straight semi-final appearance in 2016, having done so at the Monte Carlo Masters and then the recent Madrid Masters.
In windy conditions, and with red clay dust flying about, both players exchanged breaks at the start of the first set, but Murray took control after that.
The Scot used his backhand to good effect, especially on the return of serve, and was also helped by a string of unforced errors from Goffin.
Murray broke to love to go 3-1 up and more simple mistakes from Goffin meant the Belgian had a mountain to climb. Murray clinched the first set on his serve, as a Goffin forehand into the net summed up his set.
Somehow though that woke Goffin up, as Murray pulled a forehand wide to go 3-1 down but the Briton fought back in a thrilling fifth game. Neither player gave much room for mistakes, first Murray was unable to capitalise on two break points before Goffin conceded two game points. Finally, Murray found the break for 3-2 before holding serve for 3-3.
Goffin’s first-set failings resurfaced, the Belgian broken yet again to go 4-3 down, only for Murray to twice double-fault and give the break back.
The crowd certainly enjoyed the back-and-forth, though the players themselves may not have enjoyed being out on court amid the dust.
Unsurprisingly the breaks continued, Goffin missing a routine volley to go 5-4 down before a superb cross-court forehand winner pegged Murray back to 5-5.
The longest game of the match at nearly 10 minutes put Murray 6-5 ahead with the break, despite Goffin’s hard work. It was Murray’s second opportunity to close out the match on serve and Goffin, somewhat predictably, stroked a backhand long to hand the Scot victory in 94 minutes.