By winning, the seventh-seeded Shockers (29-4) set up a much-anticipated Sunflower State showdown with Kansas on Sunday.
Baker scored 15, making 7 of 8 free throws in the last 2 minutes to allow Wichita State to hold off the Hoosiers (20-14).
Freshman reserve Zach Brown had eight of his career-high 11 points in the second half, with six coming during the Shockers' decisive run.
Kevin “Yogi” Ferrell scored 24 points for Indiana. James Blackmon Jr. added 14 points and Troy Williams and Collin Hartman had 11 apiece for the Hoosiers.