La Salle was up by 18 at the half but Kansas State come back with a strong second half to take the lead. The Wildcats never pulled away from La Salle, which was able to edge back ahead with free throws despite failing to connect on a field goal in the final 8 minutes of the game.
The 13th-seeded Explorers (23-9), who had to win a First Four game Wednesday just to get to the Kansas State game, will play 12th-seeded Mississippi Sunday, which advanced on an upset of its own. The Rebels beat fifth-seeded Wisconsin 57-46.
With Mississippi and La Salle meeting in the third round, the West Region will have at least one double-digit seeded team in the Round of 16.
Wright had 10 points in the first half as the Explorers grabbed a 44-26 lead by halftime. Kansas State, however, with Jordan Henriquez providing the firepower, pulled ahead with La Salle at 57-56 with 7:05 to go.
Even though La Salle didn't have a field goal the rest of the way, Kansas State managed just one and Wright made seven free throws for the winning margin.
The Wildcats had a final chance to tie -- and a timeout to use to set up the play -- but didn't call the timeout and Angel Rodriguez missed a shot from a crowd.
Wright's 21 points came on 6-of-6 shooting from the field and 9-of-10 from the free-throw line.
Henriquez and Shane Southwell each had 17 points for Kansas State.