Abrams sank 12 foul shots -- including three in the final 21 seconds -- and added seven rebounds, four assists and three steals for the Illini (13-1).
Illinois' free throw accuracy made up for its cold shooting from 3-point territory (4-of-14) as the Illini bounced back from their lone loss of the season to Missouri last week.
Frankie Sullivan scored 21 points off the bench, including five treys, to lead the Tigers (5-7).
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Exploding whale video goes viral on Internet