The 20-year-old, who had seen off Neil Robertson and Stephen Maguire in previous rounds, produced another composed display to fight back from two frames behind and move to within one more victory of a maiden major title.
After Yan had levelled the match at 1-1 with a clearance of 94, Bingham produced two half-century breaks on his way to opening up a 4-2 lead.
The Chinese world number 11, however, started his comeback in the seventh frame with a run of 63 before a 100 break in the ninth saw him move 5-4 in front.
Bingham, who beat Shaun Murphy 6-3 in their quarter-final, edged a tense 10th frame 72-61, having battled back from 57-4 behind.
Yan, though, regained his composure in the decider, building a superb break of 65 which left Bingham needing snookers and eventually conceding the frame and with it the match.
Yan told BBC Sport: "Today I played very good, with so many excellent long pots. I made some good breaks and controlled the cue ball."
Bingham paid tribute to Yan's "unbelievable" performance.
"I think from 4-2, he did not leave me anything and everything was hard work," Bingham said.
"I am just disappointed because I felt that I did not play that great, but, in the same breath, Yan played really well from 4-2, so hats off to him."