The 39-year-old O'Sullivan, who has been in the final for the last three years, fought back from 5-3 down to lead 9-8 but Bingham reeled off five frames in a row to get into the last four for the first time.
It has been an eventful tournament for world number two O'Sullivan who played part of his first-round match without shoes on, was reprimanded for making an obscene gesture and illegally used his chalk to help line up a shot.
Bingham, world number 10, will next play Judd Trump who overwhelmed China's Ding Junhui 13-4.
Barry Hawkins will face Shaun Murphy, the 2005 world champion, in the other last-four clash.
Hawkins, runner-up to O'Sullivan two years ago, won an epic quarter-final against former champion Neil Robertson of Australia 13-12.
(This version of the story adds details about the second semi-final)
(Reporting by Ed Osmond; editing by Toby Davis)
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