Johnson had 17 points, eight rebounds and seven assists to help the Hoosiers, seeded ninth in the conference tournament, advance to play top-seeded Illinois on Friday morning.
Trailing 71-69, Michigan turned the ball over for the 10th time in the second half on an errant outlet pass. In a must-foul situation, they clamped Johnson and sent him to the line, only to see the lead stretched to four. Michigan then failed to score at the other end.
Trayce Jackson-Davis had 24 points, eight rebounds and four blocks for Indiana to spoil coach Juwan Howard's return to the bench from suspension.
Indiana surged to the lead after a 28-4 run in the second half, led by Jackson-Davis' 19 second-half points. Michigan led 41-28 at halftime.
Michigan guard Eli Brooks gave the Wolverines a 60-43 lead with a layup at the 13:36 mark before the wheels fell off for the Wolverines.
Jackson-Davis put Indiana up 63-62, converting a pair of free throws, with 5:39 remaining.
The Wolverines are in danger of missing the NCAA Tournament field with the loss, which gives them a 17-14 record.
Michigan missed 14 of 20 tries from 3-point range and shot 37.9 percent from the field.
Hunter Dickinson had 15 points for the Wolverines, who were led by guards Devante Jones (18 points) and Brooks (17).