The 35-year-old Murray reached his first ATP Tour final since June and will face former No. 1 Daniil Medvedev.
“He’s a legend,” Medvedev said of Murray. “Today was just unbelievable, the way he won.”
Murray, the three-time Grand Slam champion who has had two hip operations, fought back from a 5-3 deficit in the deciding set. He saved two match points on his own serve and three more when his Czech opponent served for the match.
“That was one of the most amazing turnarounds I’ve had in my career,” the Scot said in his on-court interview. “I have no idea how I managed to turn that one around to be honest.”
Medvedev beat second-seeded Felix Auger-Aliassime for the second time in two weeks, this time 6-4, 7-6 (7). Medvedev also won in straight sets last week in the Rotterdam quarterfinals.
“Confidence matters, because (Auger-Aliassime) had (three) set points,” Medvedev said. “I managed to just stay in there and it was enough to win.”