Adams was 5 of 9 from the floor and 3 of 5 behind the 3-point arc. Wyoming (10-2) shot 50 percent in the opening half and finished at 44.2-percent shooting overall.
The score was tied at 13 with 7:45 left before the break when Cooke's dunk put the Cowboys ahead, and they led the rest of the way.
Southern's Joell Hopkins made a basket with 3:40 left to play for the final field goal - both teams combined for six missed shots and three turnovers to close out the game.
Adrian Rodgers led Southern with 12 points, scoring nine of those in the first half. The Jaguars are currently 0-6 in away games this season.