The Orange knocked off the top-seeded Hoosiers with a typically strong defensive showing that limited Indiana to five points in the game's opening 10 minutes.
Syracuse, which has not been to the Final Four since winning the national championship in 2003, will try to return to college basketball's big show when it takes on Marquette in a Big East Conference showdown for the East Region title on Saturday.
The Orange won their only meeting with Marquette during the regular season, recording a three-point, road victory.
Indiana became the second No. 1 seed to be knocked out of the tournament. Gonzaga lost in the third round last weekend. Louisville and Kansas will try to uphold their No. 1 seeds on Friday.
Syracuse limited the Hoosiers to 16 field goals for the entire 40 minutes. Indiana shot just 33 percent from the field and made 3-of-15 from 3-point range.
Carter-Williams added seven rebounds while Brandon Triche contributed 14 points for Syracuse (29-9).
Indiana (29-7) was led by 15 points from Victor Oladipo. Seven-foot Cody Zeller was held to 10 points on 3-of-10 shooting.