The Scot has said for several months that a deep run at a tournament was not far away and he has made good on that this week with his best string of results since he won his last title in Antwerp in 2019.
He was frustrated to lose the opening set against 6ft 11in Opelka having fought back from 1-5 in the tie-break but he kept pressing on his opponent's serve and got his reward for a 6-7 (6) 6-4 6-4 victory.
Murray has always performed well against big servers, his great returns and ability to keep the ball in play making it a strong match-up for him.
He holds a 7-0 record against Ivo Karlovic and 8-0 against John Isner, and this win means he remains unbeaten against the giants of the game.
Murray will now bid for a 47th career title against either compatriot Dan Evans in what would be a first all-British ATP Tour final or Russia's Aslan Karatsev.
He said in his on-court interview: "It's already been a great week for me. I'll go for 47 tomorrow."