Purdue lost a lead in the second half, but never its composure.
Brittany Rayburn scored 21 points and the ninth-seeded Boilermakers moved into the second round of the NCAA tournament with a 53-45 win over Kansas State on Sunday.
Drey Mingo, who overcame a life-threatening bout with meningitis earlier this season, added 16 points for the Boilermakers (21-11), who advance to play the tournament's top seed, Connecticut, on Tuesday.
''This team's been through a lot this year and we kept our head,'' said Rayburn. ''That just comes down to maturity.''
Brittany Chambers scored 18 points for Kansas State (21-11), which missed its first 12 shots. Taelor Karr added 16 points for the Wildcats.
Rayburn scored six points in a 9-0 run that broke a 36-all tie, capping it with a long 3-pointer that gave the Boilermakers a 45-36 lead with just over 5 minutes to play.
Chambers' long 3-pointer with 2:10 left pulled Kansas State to within 46-45.
But Courtney Moses hit a layup and foul shot that made it 48-45. After two Kansas State airballs, the Wildcats were forced to foul, and Purdue made its free throws down the stretch.
The Boilermakers held Kansas State to 30 percent shooting, and the Wildcats hit just six of their 23 3-point attempts.
''We stepped up on the defensive end and that really got us going offensively,'' Mingo said. ''For us to be able to do that was a booster for our team.''
Kansas State trailed until well into the second half, taking its first lead at 29-27 on a putback by Chambers with 13 1/2 minutes left.
That was part of a 14-2 run that turned a 25-17 halftime deficit into a 31-27 lead. The Boilermakers hit just one of their first 11 shots in the second half.
Kansas State outrebounded Purdue 42-27, but had just 13 second-chance points.
''We had every opportunity in the second half to pull out a victory,'' Chambers said. ''As soon as we got ahead we let them back in and we let them get ahead at the wrong time in the game.''
Kansas State didn't score for over 7 minutes to open the game, missing six attempts from 3-point range.
Purdue was almost as cold, hitting two of its first nine attempts. Karr's layup made it 5-2, and the Wildcats trailed just 7-5 midway through the first half.
Mingo was hospitalized in November with bacterial meningitis and given a 50 percent chance of survival. Just 16 days later, she returned to the court, and she has been averaging over 11 points a game for Purdue, shooting 51 percent from the floor. She hit six of her nine shots Sunday and added seven rebounds.
''Her body has been through a lot,'' said coach Sharon Versyp. ''She still gets fatigued a little bit more. So, when she has the feel, when she gets it going, she definitely will always look for (her shot).''
Neither team started a senior. The Boilermakers missed the NCAAs last season, ending a 16-year run of playing in the tournament. They had their first losing season in a quarter-century, but rebounded to finish seventh in the Big Ten this season.
Like Purdue, the Wildcats missed the tournament last season. Kansas State made a late run in the Big 12, winning three in a row including an upset of Texas A&M, to get back to the NCAAs.
Purdue will face a UConn team that has a 13-game tournament winning streak after routing Hartford 75-39 in the opening round.
''It's an opportunity for us to play at the highest level, to compete, to play as hard as possible and enjoy the experience and make it extremely competitive - the best that we can,'' said Versyp.
