Carmichael had 16 points and 15 rebounds for the fourth-seeded Redbirds (19-12), who will face No. 15 and top-seeded Wichita State (27-4) in the semifinals Saturday. Carmichael also blocked five shots.
Johnny Moran hit three 3-pointers and scored 13 points to pace the fifth-seeded Panthers (19-13), who were outrebounded 48-33.
Illinois State shot only 34.5 percent (20 of 58), but Northern Iowa was limited to 25.5 percent (14 of 55).
The Redbirds used a 9-0 run midway through the second half to seal the game. After Moran had put the Panthers ahead 31-29, Illinois State scored nine in a row for a 38-31 lead with 9:17 left.
Northern Iowa got no closer than three after that.