Bright made a pair of layups in the extra frame and Chasson Randle (19 points) drained a go-ahead 3-pointer with 1:18 remaining for the third-seeded Cardinal (23-11).
Dwight Powell added 18 points and grabbed nine rebounds, as Stanford advanced to the NIT quarterfinals. They will host fifth-seeded Nevada Wednesday.
Nic Moore finished with 25 points and Tyler Brown contributed 23 for the seventh-seeded Redbirds (21-14), who went 15-of-29 from beyond the arc in their third straight overtime contest.
Jackie Carmichael supplied 21 points and 12 rebounds in the loss.