Ding looked to be struggling to cope with the pressure of the biggest match in the sport when he lost the opening six frames but clinched the last two of the first session to give himself a foothold in the match in Sheffield, England.
The 29-year-old then made breaks of 76, 103, 89 and 86 to frustrate Selby, the 2014 world champion who is seeking a second title at the Crucible Theatre.
However, the tenacious Englishman won the last two frames, including the final one that lasted 49 minutes, to build a small cushion at the halfway stage of the match.
The first player to 18 frames will win the world title on Monday.
(Reporting by Ed Osmond; Editing by Peter Rutherford)
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