Thomas Robinson bullied his way for 16 points and 13 rebounds, and the second-seeded Jayhawks rolled to a 65-50 victory over Detroit in the second round of the Midwest Regional.
''I didn't make a point of it because sometimes you make a point, it could add pressure, saying it's possible. But I did say, 'Hey, the one thing is we have to make sure Detroit doesn't play well,' '' Self said of the earlier upsets. ''When teams get comfortable anything can happen.''
After the first 15 minutes, Detroit never looked comfortable.
Doug Anderson led the Horizon League-champion Titans with 15 points before fouling out with 11:06 left. Ray McCallum, the son of the Detroit coach, added eight points on 4-for-15 shooting.
''I'm really proud of my guys,'' said Detroit coach Ray McCallum. ''We played one of the truly great teams in the country tonight, and that really, pretty much tells the story.''
Elijah Johnson added 15 points and Tyshawn Taylor had 10 for the Jayhawks (28-6), despite spending much of the second half in the locker room with cramps. Self said that Taylor received IV fluids during the game and should be 100 percent for Sunday night's game against Purdue.
Kansas toyed with the Titans (22-14) early on before ramping up the defense, eventually holding them to 32 percent shooting and 3 for 17 from beyond the arc.
''They do a good job of not letting you get in the paint. That's one of the strengths of my game,'' the younger McCallum said. ''I felt like I got good looks. It was just one of those games.''
McCallum said he watched Norfolk State's win over Missouri on the same floor in Omaha earlier in the day. He also knew that Lehigh had upset the Blue Devils.
Kansas restored some order on one of the maddest days of March Madness.
The Jayhawks used a 13-2 run late in the first half to seize control and opened the second half with a 16-4 charge that allowed them to coast the rest of the way.
''I think Missouri grabbed our attention more than anything. We were sitting there watching the game chilling at the hotel. We were definitely shocked and surprised,'' Taylor said.
This is the third time that Kansas has opened an NCAA tournament in Nebraska, and both times before it was the start of a title run. The Jayhawks played their opening games in Lincoln in 1988 and Omaha in 2008, when they won their most recent national championship.
They certainly looked like title contenders against Detroit.
After a basket by McCallum and a steal that turned into a soaring reverse dunk by Anderson, the Titans had managed to pull ahead 21-19 with 9 minutes left in the first half.
It wound up being their high point of their night.
Robinson answered with a dunk of his own — he had four dunks en route to 12 first-half points — to start a 13-2 run by Kansas. Robinson added another dunk a couple minutes later, and his basket with 2:22 remaining in the half made it 32-23.
The Jayhawks managed to build their advantage using some creative lineups.
Johnson sat all but eight minutes of the first half, and 7-footer Jeff Withey and fellow starter Travis Releford also sat long stretches, while seldom-used guard Naadir Tharpe was given the most minutes he'd played in a game since mid-February.
Self went back to his starters in the second half, but the Jayhawks didn't slow down.
Johnson drove to the rim for a basket, and after Anderson answered for Detroit, Robinson got loose for a bunny, Withey went to the foul line and Johnson's open 3 made it 42-26.
Detroit coach Ray McCallum had no choice but to call timeout.
It didn't do much good.
The 3-pointers started falling for Kansas in short order: Releford unloaded one for his first points of the game, Johnson hit his third, and Teahan let one go in transition from just in front of the Kansas bench, making it 53-28 with just over 13 minutes remaining
Many in the arena cleared out in the closing minutes as Detroit played out its season.
The Titans were making their first NCAA tournament appearance since 1999, when they beat UCLA as a No. 12 seed, but the regular-season Big 12 champions made sure it was a short stay.
''We went through a 20-minute stretch I thought we played really, really well,'' Self said. ''I'm happy with our guys. It was a good win, especially on a crazy day in the tournament.''