Ty Roberts hit his only free throw for the Cougars, giving him 24 straight to start his career, matching Klay Thompson for the WSU record.
Rodman hit a 3-pointer to start a 10-0 run that gave the Cougars the lead for good 22-13. Andrej Jakimovski followed with a 3-pointer and Gueye got two buckets inside, including a dunk.
Weber State (8-1), one of 12 undefeated teams starting the day, scored seven-straight, pulling within 26-23 on Dillon Jones' three-point play at 3:01 but the Cougars closed the half with a 9-1 surge to go up 35-24.