Illinois closed within 62-61 on a 3-pointer by D.J. Richardson with 44 seconds to play but the Tigers then went on their streak that started with a layup by Bowers.
Mike Tisdale was called for a flagrant foul on Bowers, who then hit two free throws to boost the Missouri lead to five.
Marcus Denmon had 15 points to lead Missouri in scoring. Bowers produced 13 points and Ricardo Ratliffe added 12. Missouri (11-1) has won six straight since losing in overtime to Georgetown Nov. 30.
Illinois (10-3), which has lost two in a row, got 17 points from Mike Davis.