Tate Sorensen scored 11 points for the Thunderbirds (4-2), who shot 53 percent from the field and forced 21 turnovers.
Southern Utah led 42-33 with 16:38 left, but Denver rallied with an 11-0 run.
Cox hit consecutive 3-pointers from the left wing, and Walker hit another from the top of the key. Cox made a layup with 12:43 to play, putting the Pioneers ahead 44-42.
Denver went cold from the field during the next nine minutes. After Cox s layup, the Pioneers managed just four free throws and Walker s jumper from the right baseline until Nate Rohnert made his only field goal, a layup with 3:42 left.
Meanwhile, the Thunderbirds staged a decisive 21-6 run that included 3-pointers by Allen, Barnes and Marcus Carson, and a crowd-pleasing dunk by Allen on a long alley-oop pass from Barnes.
Barnes kept the spurt going with a steal and a layup, and then hit a fall-away bank shot from the right wing that gave Southern Utah a 63-50 lead with 4:11 left.
The Pioneers tried to get back into the game by fouling down the stretch, but Allen went 8-for-8 from the foul line in the last three minutes.