It was part of the East Region and was played at the BJCC Arena in Birmingham, Ala.
Regulation ended in a 63-63 tie after Butler's Willie Veasley tipped in a missed shot with 35 seconds left.
Chism's go-ahead basket gave UT the lead for good at 70-68 with 54 seconds remaining in overtime. Chism also had four rebounds and three blocked shots.
Tyler Smith scored 15 points with eight rebounds and JaJuan Smith added 11 points and five rebounds for the second-seeded Volunteers (31-4), who will play in a Sweet 16 contest Thursday in Charlotte against Louisville, which beat Oklahoma 78-48 Sunday.
A.J. Graves led Butler with 21 points, three rebounds and two assists.
The 7th-seeded Bulldogs finished 30-4.