Junior Chris Payne scored on a 2-yard touchdown run with 44 seconds left in the quarter to help give St. X a 26-7 lead.
Hinsdale, a team from suburban Chicago, scored on a fumble recovery in the third quarter to close the gap to 26-14.
Senior Donny Stock added a 25-yard field goal with 1:26 left in the third quarter to extend the Bombers’ lead to 29-14.
St. X went ahead 36-14 after Wolf found Andrew Wittrock for a 31-yard touchdown pass connection with 9:52 left in the fourth quarter.
The Bombers went ahead 43-14 when Fox scored on a 2-yard touchdown run with 3:03 left.
Fox finished with 21 carries for 172 yards and two touchdowns.
St. X, the reigning Division I state champion, is 11-3 in the Showdown since 2004 and has only one loss to an Ohio team in that span in the event (Colerain in 2008).
St. Xavier is ranked No. 18 nationally by the MaxPreps Xcellent 25 rankings (editorial rankings). The Bombers are No. 6 in the USA Today Midwest computer rankings.
St. X plays at Colerain at 7 p.m. Sept. 1. It will be the 35th meeting between the programs. Colerain won the regular season game in overtime in 2016 but St. Xavier won the regional semifinal game in overtime.