Western State jumped out to an early 12-4 lead following Dominique Wright's 3-point jumper. The Cowboys (2-0) took control then as Josh Adams and Matt Sellers had consecutive dunks and Jason McManamen nailed a 3-pointer to lead Wyoming on a 22-0 run and a 26-12 lead.
The Mountaineers (1-2) never fully recovered from that onslaught but they did close to 31-25 at halftime.
Cooke Jr, who made all six of his field goal attempts, slammed home two dunks to start a 9-2 run to open the second half.
The Cowboys shot 60 percent from the field in the second half, hitting on 24 of 46 attempts for the game.
Wright had 16 points, nailing 5 of 7 3-point attempts to lead Western State.