Thomas Robinson fought through double teams all night for 11 points and 13 rebounds, and the Jayhawks (29-6) got enough production from everyone else to erase a 10-point second-half deficit and reach the Midwest Regional semifinals in St. Louis.
"What a great game. It wasn't the best played, but it was a grind-it-out, typical Big Ten game," Self said. "Hummel was unbelievable, and we just hung in there."
Purdue was clinging to a 60-59 lead and had the ball and less than a minute remaining when Lewis Jackson, the shot clock winding down, lost control at the top of the key. Johnson picked it up and went the other way for the go-ahead lay-in with 23.3 seconds left.
Hummel missed an open 3-pointer at the other end, and Tyshawn Taylor scored a transition dunk for the Jayhawks with 2.5 seconds left.
After a timeout, Purdue sharpshooter Ryne Smith managed to get off a decent look at a long, potential tying 3-pointer. It hit off the backboard, clanked off the rim and finally fell away.
"It stinks," Purdue coach Matt Painter said. "It stinks to lose."
Hummel finished with 26 points and nine rebounds for the Boilermakers (22-13).
North Carolina State 66, Georgetown 63 • Lorenzo Brown hit three free throws in the final 10.6 seconds as the Wolfpack upset the third-seeded Hoyas in Columbus, Ohio.
A lowly 11th seed coming in, they had to survive a furious comeback by the Hoyas (24-9) and were assured of the win only when Jason Clark's hurried 3-point attempt from the right wing was off the mark at the buzzer.
Hollis Thompson led the Hoyas with 23 points.
North Carolina 87, Creighton 73 • John Henson posted 13 points, 10 rebounds and four blocks in his return from a wrist injury, but Kendall Marshall broke a bone in his right wrist during the second half of North Carolina's victory in Greensboro, N.C.
Dennis Marshall, Kendall's father, told CBS.com on Sunday night that his son would have surgery Monday morning to insert a screw in the injured wrist. The point guard still finished with 18 points and 11 assists.
Ohio 62, South Florida 56 • Walter Offutt scored 21 points and D.J. Cooper added 19 as No. 13 seed Ohio won in Nashville, Tenn.
In the final 36 seconds, Cooper went 3-for-4 from the line and the Bulls missed three shots.