Jeff Elorriaga scored 21 points and made five 3-point baskets and Mikey Thompson added 16 points and five steals for the Broncos (3-0).
Jarell Flora scored 21 points and made six 3-pointers to pace the Redhawks (2-2). Deshaun Sunderhaus added 11 points for Seattle, which committed 17 turnovers.
The Redhawks trailed only 46-43 after Flora's 3-pointer with 15:53 remaining before Boise State went on a 13-4 run. Drmic scored eight points during the surge and Elorriaga drained a 3-pointer as the Broncos opened up a 59-47 lead with 10:44 left.
Boise State's lead reached 69-52 with 4:04 to play after a 3-pointer by Thompson and four free throws by Drmic. The Broncos' largest advantage was 21 points.
Drmic was only 5-of-15 from the field but hit 14-of-18 free throws.
Elorriaga scored 13 points in the first half and Thompson added 11 as the Broncos held a 39-32 halftime advantage. Flora made four first-half 3-pointers while scoring 13 for the Redhawks.
Seattle made a strong push at the beginning of the second half to move within three before the Broncos controlled the remainder of the contest and repeatedly went to the free-throw line. Boise State was 23-of-27 from the in the second half to finish 27-of-33 overall.
Seattle shot just 10 free throws in the contest, making six. The Redhawks were 8-of-28 from 3-point range.
Derrick Marks added 10 points for the Broncos, who committed just six turnovers while racking up 13 steals. Drmic had four thefts and Marks had three.
Jack Crook with 10 points and 10 rebounds and Isiah Umipig with 10 points and eight assists also scored in double digits for Seattle.
A 3-pointer by Flora gave Seattle a 14-13 lead with 13:17 left in the half before Boise State scored three baskets in 35 seconds to take a five-point lead. The lead was extended to 39-26 on Thompson's basket with 1:15 left before Seattle tallied the final six points of the half to trail by seven.