ASU's Taylor Lamb threw a 2-yard touchdown pass to Simms McElfresh in the back corner of the end zone to get the Mountaineers within a point. But Zach Matics, who had a field goal blocked and missed two others, had his extra point attempt swatted away by McCullum, capping a frantic final 8 minutes.
Appalachian State (1-2) tied the game at 14 on a 10-yard touchdown pass from Lamb to Malachi Jones with 5:08 to play.
It was only the third catch of the sophomore's career and his first this season, as Mullens caught the Mountaineers in an all-out blitz on third down and flipped the ball to a wide-open Payne down the left sideline.
Payne scored on runs of 15- and 3-yards in the first half to give the Golden Eagles a 14-7 halftime lead.
Running back Marcus Cox, who rushed for 119 yards on 22 carries, scored on a 5-yard run in the second quarter for the Mountaineers.
Lamb, in his first career start, completed 28 of 40 passes for 264 yards. The freshman threw two touchdowns with two interceptions.
Mullens completed 22 of 35 passes for 268 yards with a touchdown and two interceptions.
Appalachian State, playing its first year as a Football Bowl Subdivision member, outgained the Golden Eagles 455 total yards to 329 total, ripped off 26 more snaps and had nearly a 12-minute advantage in time of possession.
But Matics missed field goals of 43 yards and 42 yards and had 36-yarder blocked by defensive end Will Freeman. The Mountaineers also lost a red-zone opportunity when McCullum stripped Cox of the ball at the USM 7 on Appalachian State's first play following a Mullens' interception.
Southern Miss, which managed just one victory in 24 games during the 2012 and 2013 season, picked up its second home win of the year and broke even on its non-conference schedule.