The Greenbacks led from a tenth minute Matty Lee drive before Sam Bircher made the most of a mistake in the Sphinx defence and banged home from close range.
In the 22nd minute, Mark Withers added a third and two minutes later, Bircher made the most of a mistake to net his second of the game.
Sphinx rallied but conceded a penalty in the 73rd minute to a Bedworth side which had lost keeper Simon Harris. Sam Taggart who was pulled down got up to score.
With six minutes to go, Dean Kimberlin blasted home from close range to pull one back for Sphinx and in the next attack, Gianni Dainty scored from a corner to reduce Bedworth's margin of victory.
Sphinx are away to Redditch United on Wednesday but will be at home to the Greenbacks in the League Cup,a fortnight today.
Teams
Sphinx
Hindmarsh, Goodbody (Jones),Jordan (Mead),Kay,Mulholland,Barrett (Collins), Kimberlin,Pittaway,Elvridge,Wallace,Dainty SNU Price,Handley
Bedworth
Harris,Thorpe,Wagstaff,Lee,Ring,Jephcott,Troop,Taggart,Bircher,Keating, Withers Subs Domole,Chambers,Hill,Collier