With John Woodhouse taking the team due to Paul Charnley and Danny McSheffrey being at the Grand National, Sphinx trailed to a 20th minute Craig Gregg goal.
Straight after the restart, Gregg scored again to give the Shropshire side the victory.
On Tuesday night, Sphinx are at home to Market Drayton Town in the Midland Alliance League Cup Semi-Final Second Leg. Sphinx trail 4-0 from the first leg.
Coventry Sphinx Reserves beat Highgate United 5-1 at Sphinx Drive with Jerome Murdock hitting a hat-trick.