Stanford and Santa Clara were not selected for the NCAA tournament Sunday but were picked to participate in two other postseason events.
Stanford will open defense of its NIT championship at 8 p.m. Tuesday against Stephen F. Austin at Maples Pavilion. Santa Clara will host Vermont in the College Basketball Invitational at 7 p.m. Tuesday. Both teams have 21-11 records.
The SCU-Vermont winner advances to a game next Monday against the winner of a first-round game matching Western Illinois and Purdue.
Stanford, which defeated Minnesota 75-51 in last year's NIT final, was given a No. 4 seed in this year's tournament. Kentucky, Alabama, Southern Mississippi and Virginia are the No. 1 seeds.
Tuesday's game, to be shown on ESPN2, will be the first meeting between Stanford (18-14) and Stephen F. Austin (27-4) of the Southland Conference.
The winner of Tuesday's game plays the winner of a game between Alabama and Northeastern at a date and site to be determined.
The 32-team NIT field includes two other Pac-12 teams in No. 3 seed Arizona State and No. 6 seed Washington.
The first three rounds are played at campus sites, with the semifinals and championship game played at Madison
Kentucky, last season's NCAA champion, will have to play at eighth-seeded Robert Morris on Tuesday. Rupp Arena is unavailable to the Wildcats because NCAA games are being played there later this week.
The Associated Press contributed to this report.