After Chandler Stanton's 45-yard field goal put the Mountaineers on top with 5:45 to play, the defense held but Robert Lefevre's 45-yard punt pinned Appalachian State on its 8-yard line with four minutes remaining.
Noel then carried five-straight times, the last two 41- and 22-yard bursts that put the Mountaineers (3-1) on the Marshall 5. Quarterback Chase Brice then knelt down three times to run out the clock.
After the second of Brice's touchdowns, Rasheen Ali had a 97-yard kickoff return to give Marshall a 20-14 lead. But Brice capped a third long drive with a touchdown two seconds before halftime to put Appalachian State back on top 21-20.
Ali's touchdown run gave Marshall (2-2) a 30-21 lead entering the fourth quarter.
The former conference rivals from the FCS days were meeting for the second time as FBS schools with Marshall winning 17-7 last season.
Swanson's pick-6 in 4th gets Troy past Texas State 31-28
— Kimani Vidal ran for 162 yards and two touchdowns, Keyshawn Swanson had a fourth-quarter interception return for a touchdown, and Troy beat Texas State 31-28 on Saturday.
College football today - Week 7 updates, highlights, biggest moments and more
Here are the best moments on and off the field from college football's Week 7.
Ball State holds off E. Michigan 38-31; Hall sets FBS mark
— Drew Plitt passed for 207 yards and a touchdown, Justin Hall rushed for two scores and Ball State eked out a 38-31 win against Eastern Michigan on Saturday.
Mayer throws 3 TD passes, Miami of Ohio beats Akron 34-21
— AJ Mayer threw two of his three touchdown passes in the first quarter as Miami of Ohio jumped out early and beat Akron 34-21 on Saturday.
Miller Carries Columbia Past Penn - Via Ivy League
Dante Miller ran for 187 yards and a touchdown to help Columbia defeat Penn in Ivy League play
'No way!' Florida A&M WR has TD fall into his lap on unreal play
Florida A&M receiver Chad Hunter battles for the ball and turns a near interception into a sensational touchdown.