Oladipo's long jumper off an assist from Yogi Ferrell extended the Hoosiers' tenuous 1-point lead and proved to be the decisive blow as Indiana (29-6) advanced to the East Regional semifinals.
They will next take on fourth-seeded Syracuse Thursday in Washington.
Oladipo finished with 16 points and grabbed eight rebounds while Will Sheehey added 10 off the bench for the Hoosiers, who advanced to the Sweet 16 for the second straight year.
Khalif Wyatt pumped in 31 points but committed a key late foul for the ninth-seeded Owls (24-10), who surrendered the final 10 points of the contest after leading by four late in the second half.
Wisconsin business offering 'therapeutic cuddling' forced to close
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]