The Cowboys must play at Pullman, Wash., because they are the lower seeded team, and in the NIT the higher seeded teams play on their home courts. OSU is a No. 3 seed, while Washington State is a No. 2.
The winner of Monday night's game between the Cowboys and Cougars will advance to a third-round game next Wednesday or Thursday against No. 1 seed Boston College (21-12) or No. 4 seed Northwestern (19-13).
The Cougars, led by second-year head coach Ken Bone, finished 9-9 in the Pac-10.
"This first win is huge," Bone said following Wednesday night's victory over Long Beach State. "I think now we will have time to focus on Oklahoma State, like they will us.
"I think our guys will be in tune, and think, 'hey, two more wins and we get to to go New York City, play in Madison Square Garden,' which is something every basketball player dreams of."
Other Second-Round Matchups
Boston College (21-12) vs. Northwestern (19-13), Saturday, 10 a.m. (ESPN)
Virginia Tech (22-11) vs. Wichita State (25-8), Sunday, 10 a.m. (ESPN)
College of Charleston (25-10) vs. Cleveland State (27-8), Saturday, 1 p.m. (ESPNU)
Alabama (22-11) vs. New Mexico (22-12), Monday, 8 p.m. (ESPN)
Missouri State (26-8) vs. Miami (Fla.) (20-14), Monday, 6 p.m. (ESPN)
Colorado (22-13) vs. California (18-14), Friday, 8:30 p.m. (ESPNU)
Fairfield (25-7) vs. Kent State (24-11), Sunday, 11:30 a.m. (ESPNU)