Selby edged a scrappy first frame, but could only piece together 26 points in the next three frames as Yan's matchplay saw him head for the mid-session interval holding a 3-1 lead at the Marshall Arena in Milton Keynes.
Breaks of 99, 119 and 61 were enough to give Selby the edge at 4-3 ahead as he finally ran into some form, but a 68 run from Yan restored parity at 4-4 before the evening session.
“To be fair, the first four frames before the interval, pathetic really,” said Selby.
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“But then after that I felt as though I got into the match, tried to pick up the momentum and find some tempo.
"And I felt as though from three-one to win the match nine-six, I didn’t really do too much wrong.
“Yes, I missed a few balls, but I think we’re going to.
“We’ve not played that many matches for a while. So it’s understandable, but from three-one I felt as though I played okay.
“And I’m happy enough with my performance from three-one, if you cancel out the first four frames.”
Selby emerged the stronger figure upon the resumption of the evening session. He made 66, 57, 64 – including a huge fluke on the final black in winning the 12th frame – and a 105 break to move 8-5 clear.
World number 16 Yan made 51 to reduce his arrears to 8-6, but Selby kept his composure in the 15th frame to see out the match with a tricky pot on the final red with a rest down the cushion giving him the platform to finish off the match in his favour against the Riga Masters winner.
The former world number one will face Shaun Murphy or Mark Allen in the last four on Thursday.

Tour Championship draw (best of 17 frames)

(All sessions start at 1:30pm and 7pm BST)
  • Neil Robertson 5-9 Stephen Maguire (Saturday)
  • Judd Trump 9-4 John Higgins (Sunday)
  • Mark Selby 9-6 Yan Bingtao (Monday)
  • Shaun Murphy v Mark Allen (Tuesday)
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