Foul trouble plagued the Wildcats, too, as Spradling and leading scorer Marcus Foster sat out much of the first half with two fouls.
"We had some unconventional lineups in there," Weber said. "But they didn't go down. They kept battling."
Foster ended the first half with two points on the opening basket of the game and finished with 11. Thomas Gipson and D.J. Johnson both scored 12 for Kansas State.
Ejim, the Big 12's leading scorer with an average of 18.4 points, opened the second half with a three-point play.
Kansas State pushed its advantage to five before the Cyclones rallied to take their first lead in nearly 23 minutes. But the Wildcats answered in the closing minutes, and Spradling's 3-pointer with 1:38 remaining gave them a 72-69 edge they did not relinquish.
"Their two shooters made big shots when they needed them," Hoiberg said. "Spradling came off after struggling and knocks a big one down. Foster did the same thing the next time down. That's what great players do, a four-year player in Spradling and one of the best freshmen I've seen in a long time in Foster."
Kansas State closed it out with six free throws in the final 1:23.
"They came right back and hit some big shots," Ejim said. "We played hard, guys came in, stepped up and made some big shots, but truly they were able to make some big shots down the stretch and make some stops."
A 12-point first half from Southwell was a welcomed sight for the senior as he broke out of a monthlong slump. His 13 points were his most since scoring 14 at Iowa State on Jan. 25.