Bingham, aiming for the historic feat at age 47, struggled to replicate the form that saw him upset Ronnie O'Sullivan in the previous round. Jones, ranked 44th, remained composed throughout the encounter to set up an unlikely final against Kyren Wilson on Sunday.
The turning point came on Saturday evening. Bingham, trailing 13-11, missed a crucial long green and black off the spot. He then attempted a risky safety shot on the green after a sensational yellow pot, which backfired spectacularly.
Instead of closing the gap, Bingham's error allowed Jones to extend his lead to 14-11. Jones never looked back, compiling breaks of 66, 70, and 58 to seal a memorable victory and book his place in the final.
Speaking after his victory, an emotional Jones spoke of his pride at reaching the final of one of snooker's biggest events.
"When I think of watching the World Championship final every year, thinking it's a dream and what an unbelievable occasion it is, it doesn't really feel real that I'm in that World final," Jones told the BBC.
"But I am - and I couldn't be any happier."
"It's not been easy to get here. There are a lot of good players on the Tour and I haven't made a quarter-final all season and I didn't really come here with any confidence or sharpness.
"I don't think I'm playing well - I'm just winning. I'm not doing anything exceptional at all - I'm not scoring heavy really - I'm making 60s or 70s but I'm not doing anything special. If you keep winning those frames, they are big and they hurt your opponent."
Bingham, the heavy favourite to advance to the final, was left to rue his missed opportunity, describing his performance as "embarrassing" and claiming he didn't enjoy his time at the table.
"It was embarrassing really," the world number 29 told the BBC.
"I must have given eight frames away. I must have missed eight or nine blacks off the spot. I'm very disappointed after playing like I did against Ronnie. Just didn't enjoy it out there."
Wilson dominantly overcame David Gilbert earlier on Saturday to book his place in the final.
