Murray was forced to call on all his reserves at times against a French opponent 11 years his junior before prevailing 3-6 7-5 6-2 in just over two-and-a-half hours.
The three-time grand slam champion, still on the road to full recovery following career-saving hip surgery in January, now faces old foe Stan Wawrinka in Sunday's final in what will be his fourth match in as many days.
Murray's clash with Humbert, 21, was his first semi-final since the 2017 French Open, when he lost to Wawrinka.
"It's been a long road to get back to this point," Murray, 32, told Amazon Prime. "I certainly didn't expect it to come so soon since I started playing again.
"It's been a big surprise to me and I'm happy to be through to the final."
The Scot added: "Stan's a brilliant player. We've played against each other in some big matches in the past in big tournaments.
"He's had his injury troubles as well the last couple of years and done great to get back to the top of the game.
"It was actually my match with him at the French Open in 2017 when my hip problems really started.
"It was a tough five-set match in the semis and my hip never really recovered from that, so it's cool to be back playing against him in a final."
Murray spurned two break points at 2-2 in the first set and was made to pay when he was broken in his next service game to trail 4-2 before Humbert served out to clinch the first set 6-3 after 41 minutes.
Murray broke Humbert to lead 3-1 in the second and was pegged back to 3-3 and 5-5, when the two-time Wimbledon winner began to flex his elbow, which was feeling the effects of a hectic schedule.
The Scot edged 6-5 in front and in the decisive game he pounced when Humbert faltered.
Two wayward forehands helped hand Murray three break points and he converted the third as the Frenchman double-faulted to take the set 7-5 and level the match.
Murray dug deep to take the opening game of the deciding set after saving three break points, and went on to make it five games in a row as he opened up a 3-0 lead in the decider.
He dictated more of the rallies as Humbert lost his way and moved 4-1 and 5-2 ahead before taking the contest on the first of two match points.