Wanderers have a few early chances to take the lead in this cup tie, with King-Harmes and Sterling coming close but not enough to break the deadlock.
However, the Clarets took the lead just after the half hour mark with Michael Fowler firing home from close range after a defensive error.
Soon after and Burnley had their second with Fowler scoring his second of the afternoon.
The forward managed to curl the ball into the bottom corner past Matthew Alexander.
Nicky Spooner's men soon bounced back through Matthew Argent-Barnes, as he was brought down in the penalty and ultimately dispatched the spot kick.
As the second half began, Wanderers U18s came out dominating possession.
Five minutes into the second half and King-Harmes received the ball wide and cut in from the right beating the goalkeeper from all of 25 yards.
Both sides began to search for the equaliser, but it was Burnley who found the winner with five minutes to go.
It was that Fowler who sealed his hattrick, as Udoka Chima played a long ball through to the forward who placed the ball past Alexander in the Wanderers goal.
Wanderers XI: Alexander, Whalley, Edmondson, Graham, Senior, Preston, King-Harmes, Riley, Sterling, Darcy, Barnes.
Substitutes: Smith, James, White, Richards