Rice scored on a pair of 7-yard runs and added a 63-yard burst before his 1-yard plung in the first minute of the fourth quarter to make it 27-10.
The Catamounts (7-4, 5-3 Southern Conference) mounted a comeback and pulled within three on Brody Palhegyi's 4-yard run with nine minutes to go. But the Keydets (5-6, 4-4) responded by chewing up more than seven minutes before missing a field goal.
Western Carolina picked up a first down before the drive stalled out near midfield with a minute left.
The Catamounts were looking for an eighth victory for the first time since 1984 and six conference wins would have been the most in their 47 years in the SoCon.
Collin Ironside threw for 194 yards with Aidan Twombly accounting for 133 yards on six catches.
Palhegyi was 18 of 31 for 254 yards, a touchdown and an interception, and he picked up 80 yards on the ground.
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