Wade defeated Ireland’s Connie Finnan by three sets to two, while Whitlock swept past Ronnie Baxter in straight sets.
They will now go head to head on Friday for a place in the semi-finals.
Full match reports can be read on the players’ official websites via the links below.
Paul Nicholson lost out at the hands of Phil Taylor, suffering a 3-1 defeat after missing two darts to take it to a deciding set.
Gary Anderson beat Wes Newton in the evening’s other match.
By Chris Murphy