Odister's foul shots capped a furious second-half comeback that saw Cal Poly overcome a 51-33 deficit with 12 minutes to play.
The Mustangs (2-2) emerged with the victory after the Bruins' Norman Powell and Jordan Adams each missed potential game-winning 3-pointers in the closing seconds.
Odister finished with 15 points and Dylan Royer drained six treys en route to an 18-point performance for Cal Poly. Brian Bennett added 16 points and Chris Eversley contributed 15 and 10 rebounds for the winners.
Shabazz Muhammad supplied a double-double of 15 points and 10 boards for the Bruins (4-2), who fell to 3-1 at home.