Murray, who had career-saving hip surgery in January, showed his trademark stubbornness to win 3-6 7-5 6-2 in two hours 23 minutes.
He will face fellow three-time Grand Slam winner Stan Wawrinka of Switzerland in Sunday’s final.
Krajinovic, ranked at 60, will be appearing in his third final but is also seeking a first career title.
It is 32-year-old Murray’s first final appearance since the Dubai Championships in March 2017, when he was then the world number one.
No player had ever returned from a hip resurfacing operation to play singles before Murray.
And he has managed to reach a final just two months after making his singles return, at Winston-Salem in August.
The Scot has played four tournaments in just over four weeks and showed signs of fatigue and frustration in the opening set.
He struggled on his serve, producing three double faults in the first six games, which allowed 21-year-old Humbert to force the first break of the match.
By contrast, Humbert wrapped up the first set with an ace, and kept up his aggressive play with some deep hitting in the second set.
The two traded breaks in the second before Humbert, serving to force a tie-break, lost his rhythm, and handed Murray the set on a double fault.
Five games in a row went to Murray, allowing him to open up a 3-0 lead in the decider, and his serving grew stronger as the match progressed.
He appeared to have some trouble with his right elbow, which may have affected his serve, but he finished the match with six aces and won 77% of points on his first serve.
Murray holds an 11-8 head-to-head record over Switzerland’s Wawrinka, 34, and both players have struggled with injuries in recent years.
The Scot injured his hip in his 2017 French Open semi-final against Wawrinka, while the Swiss had a disrupted two years with a knee injury.
“Stan’s a brilliant player. We’ve played against each other in some big matches in the past in big tournaments,” Murray added.
“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.”