The Scotsman next will challenge defending champion Mark Selby, who put out Northern Ireland's Mark Allen 6-5, for a place in the final.
Higgins opened up a 3-1 lead over Ding in the best-of-11 frame quarter-final but the Chinese star roared back to level at 4-4. Higgins took the next two frames to secure victory.
Earlier, Englishman Selby came from 4-2 and 5-4 behind to see off Allen's Wembley challenge.
Friday sees the conclusion of the quarter-finals with Stephen Maguire of Scotland facing Australia's Neil Robertson while world champion Ronnie O'Sullivan takes on English compatriot Ali Carter.