Murray, who is now ranked No. 243 in the world, returned to singles play in August after he underwent career-saving hip surgery in January. Entering the tournament, he was searching for his first ATP singles title since lifting the trophy at the Dubai Championship in March 2017.
Murray lost the first set but battled back to win 3-6, 6-4, 6-4, giving the Brit an emotional win in his injury-filled journey.
"It means a lot," Murray said after the match. "The last few years have been extremely difficult, both me and Stan have had a lot of injury problems in the last couple of years. It's amazing being back in a final playing against him like that. It was a great match. Stan was playing unbelievable.
"I didn't expect to be in this position at all, and I'm very, very happy."
The former world No. 1 underwent hip surgery after his first-round exit at the Australian Open. He returned to the tour to play doubles, winning the title at Queens in his first action back before teaming with Serena Williams at Wimbledon.
Murray made his singles return in August at the Winston-Salem Open. The 32-year-old is a three-time Grand Slam winner.