Higgins, a four-time world champion, overturned a slow start against Louis Heathcote to claim a 5-2 victory. Two frames down, the Scot responded with five in succession.
Selby, meanwhile, was pushed hard by fellow former world champion Mark Williams before emerging a 5-3 winner. From 3-2 adrift, Selby summoned his response, compiling a century in the sixth frame and tightening the screw in the closing stages to book his place in the last four.
Anthony McGill also advanced, producing a composed finish to beat 19-year-old Stan Moody 5-3. The Scot trailed late in the match, but steadied himself with two well-timed breaks along the way to seal the win.
Shaun Murphy rounded off the quarter-final line-up with the most emphatic result of the day, brushing past Mitchell Mann 5-1 in little more than an hour.
With Higgins, Selby, McGill and Murphy through, the tournament heads into the weekend with a distinctly heavyweight cast -- Selby set to face Murphy, and Higgins taking on McGill.