Brown also had 13 rebounds and Cougill 10 for the Phoenix (2-0), who took control of the game with a 12-0 run that put them ahead 23-8 in the first half. Keifer Sykes added 13 points and Carrington Love had 11.
Jackson Stevenett led Southern Utah (0-2) with 15 points.
Green Bay shot just 37.7 percent from the floor but committed only nine turnovers and outrebounded the Thunderbirds 51-40.
Southern Utah, which committed 28 turnovers in a season-opening 103-65 loss to Gonzaga, had only 13 this time around. But the Thunderbirds shot 34.5 percent, including a 4 for 17 showing from 3-point range.