The contest, played at the new Cowboys Stadium, built by Dallas Owner Jerry Jones, featured seven pass interceptions, including four by State's Zac Robinson and three for Ole Miss counterpart Jevan Snead.
McCluster rushed for 185 yards on 34 carries. He scored on an 86-yard, second-quarter run and a 2-yarder in the fourth, the go-ahead touchdown from a 7-7 tie with 4:03 remaining.
Patrick Trahan scored on a 34-yard, fourth-quarter fumble return, and Shay Hodge caught seven passes for 112 yards for the Rebels (9-4), who recorded their second straight bowl victory.
Robinson completed 13-of-31 passes for 118 yards, backup Keith Toston passed for 41 yards with one touchdown. Josh Cooper and Justin Blackmon combined to make eight receptions for 96 yards for the Cowboys (9-4), who were out-gained by 365 yards to 255.