Wimbledon and Olympic champion Murray, who had won all five of his previous meetings with the 11th-ranked Belgian, was beaten 7-6 (7/4), 6-4.
“I served really well and that was key to staying in the match,” said 26-year-old Goffin who will face Rafael Nadal in Saturday’s final.
“Andy returns so well, puts the pressure on you so that makes it tough to serve well all the match.
Nadal downed Canada’s Milos Raonic, the world number three, 6-1, 3-6, 6-3 in his semi-final as the 14-time major winner looks to end an injury-hit 2016 with a fourth UAE title on Saturday.
Nadal, 30, defeated Raonic for the seventh time in eight career meetings.
“It’s great to be back on court after a time without matches,” said Spanish great Nadal, a former world number one who is now down at nine in the rankings.
“To beat two great players (Tomas Berdych on Thursday and Raonic on Friday) is great news for me.”
Nadal and Goffin will meet for the first time on Saturday.
“David is very talented. It will be a tough match but I will do my best,” said Nadal.
In the match for fifth-place in the six-man field, France’s Jo-Wilfried Tsonga beat Czech Thomas Berdych 6-7 (5/7), 6-3, 10-3.