Chris O'Shea opened the scoring for Nigel Starkey's side in the 36th minute with Tom Rawlings adding a second in the second half.
Sphinx now play Dosthill Senior Colts at home in the next round.
Sphinx travel to Swindon Town on Tuesday night for their FA Youth Cup Second Round tie. Kick Off at 7.30pm and have been drawn at home to Stroud in the Midland Floodlit Youth League Cup Third Round.