Taking three of the four opening frames in Preston, former world champion Higgins secured breaks of 68 and 58.
Selby impressively responded with breaks of 67 and 76, and then a further score of 121 to take the lead.
Two more half-centuries put Higgins back on course for victory, and he closed it out to progress to the next round against O’Sullivan.
There was also a 6-4 victory for Stuart Bingham, over David Gilbert, which means he will next meet Mark Allen.
Judd Trump progressed to the semi-finals, after recovering from a losing position to win 6-5 against Jack Lisowski.