Humphries won the first set against Clemens despite averaging just 89.82, but was more purposeful in going 2-0 up with a second-set average of 108.59.
He also claimed the third set but the signs of Clemens sparking into life were there.
The German reached the semi-finals in 2023 but had failed to progress past round three in the past two years.
He won the fourth set without dropping a leg, and took out 121 and 116 finishes.
Clemens also claimed set five and at this stage he was on a roll, winning eight of 11 legs across sets three to five.
This was not a case of Humphries’ level dropping – he took out 170 in set five and averaged 103.25 and 110.25 in the two that Clemens won.
Clemens had three darts at double 20 to earn a deciding set but went inside on 20 and 10 before going high on the double five.
Humphries needed 81 to secure his passage and, after nailing double 13 with his final dart, wheeled off in celebration and jumped around the stage fist-pumping in a rare showing of emotion and relief for the world number two.
“I don’t think I really dropped off but Gabriel got a lot better,” Humphries, who averaged 100.14 to Clemens’ 101.49, told Sky Sports.
“If that double 13 doesn’t go in, it is 3-3 and I’m panicking.
“That could be the difference between being world champion again or not.
“I just found another level there when I needed it.”