Trump trails his 20-year-old opponent 5-3 after the first session in their best-of-25 encounter – although it could have been worse had he not clinched the final frame.
Yan, who has lost all five previous meetings with Trump, made a total clearance of 133 and breaks of 91 and 93 in an impressive display.
'I need to be patient' - McGill on defeat to Bingham at Crucible
Trump is bidding to become the maiden first-time champion to defend a world title in the Crucible era.
Yan Bingtao makes 133 total clearance at World Snooker Championship
Meanwhile, Stuart Bingham and Mark Williams are locked at 8-8 ahead of their final session.
Bingham rattled off four frames on the spin to turn 3-6 into 7-6, but three-time world champion Williams belatedly stemmed the tide to keep his hopes on track.
'Just can't wait' - Emotional Bingham on reaching semi-finals
'Brilliant pot' - Trump sinks outrageous long red from cushion