Higgins recovered from 9-4 down to produce one of the finest comebacks of his career, reeling off six consecutive frames across Sunday evening and Monday afternoon to seize control of a match that had appeared to be slipping away.
O'Sullivan, chasing a record eighth modern-era title, briefly regained an edge with breaks in the closing stages, including an 81 to force the decider, but could not deliver the decisive blow.
In the final frame, Higgins capitalised after an early chance went begging, composing a match-winning contribution to clinch a memorable victory to a standing ovation.
“I came to the party at last,” said the Scot. “At 6-2 down, I felt if I could win a couple of frames, I had a chance.”
“Of course I’m disappointed,” O’Sullivan said. “I felt I was in a better place than I have been for a while, but over the match I don’t think I was the better player and I just missed too many key balls.”
Higgins advances to the quarter-finals, where he'll face Chris Wakelin or Neil Robertson.
Selby beaten by Wu
On the other table, Wu Yize produced a surprising 13-11 win over four-time world champion Mark Selby.
The Chinese starlet built on an overnight lead of 9-7 and withstood repeated pressure as Selby threatened several comebacks, including breaks of 89 and 95.
Selby twice narrowed the gap, but errors at crucial stages proved decisive. Wu edged clear again at 12-9 before Selby rallied once more, only to falter when chances to level arose.
A break of 53 in the final frame settled matters, sealing Wu progress to the quarters, where he'll meet Judd Trump or Hossein Vafaei.