Southwick completed 18-of-27 passes for 195 yards with an interception as the Broncos (4-1) posted an easy victory despite converting just 2-of-11 third downs.
Southwick threw scoring strikes to Chris Potter, Kirby Moore and Matt Miller.
D.J. Harper added a pair of rushing TDs en route to 47 yards for Boise State.
Desmond Johnson led the Golden Eagles (0-5) with 116 rushing yards and a touchdown on 15 carries.