Two-time winner Wade claimed a comfortable win against the Scotsman, taking his sixth victory over the last three days.
Wade produced an early 126 checkout as he took the first three legs without reply.
Henderson took two of the next three but Wade took command with another three on the spin to move 7-2 ahead.
The Scotsman pulled another leg back but ‘The Machine’ sealed a place in the last eight by winning two of the final three legs.
“I wasn’t at my best and it was lucky for me that John wasn’t either,” said Wade, who won the tournament in 2008 and 2011.
“There is massive strength in depth in the PDC at the moment so it is a huge achievement for me to be in the quarter-finals.
“I’ve just been taking one game at a time and that is all I can continue to do.”