The rest of the Cyclones shot 6 for 35 (17 percent) from the field in an 80-73 loss to Kansas State, which put five players in double figures.
''You look at 38-2 on bench points, that's a pretty telling stat right there,'' Iowa State coach Fred Hoiberg said. ''They did a great job.''
Will Spradling hit a tiebreaking 3-pointer with 1:38 left for Kansas State (20-9, 10-6 Big 12), in a four-way tie for second place in the conference with Iowa State, Oklahoma and Texas.
Shane Southwell had 13 points for the Wildcats, trying to earn the No. 2 seed in the league tournament. They play at Oklahoma State on Monday and then host Baylor on Saturday to end the regular season.
Kansas State has won 15 straight at Bramlage Coliseum, its longest home winning streak since the 1981-82 season.
Ejim had 30 points and 16 rebounds, and Kane added 24 points and eight rebounds to pace the Cyclones (22-6, 10-6). Ejim, the Big 12's active leader in career double-doubles, got his 31st by halftime with 14 points and 10 rebounds.
''He really struggled in his last game and only played 20 minutes,'' Hoiberg said. ''But we stepped up in his absence and got a big win despite him being on the bench for half of the game. His energy was off the charts tonight. To go out and have 30 and 16 on the road is a pretty big-time performance.''
Behind a 16-0 run, the Wildcats opened a 20-9 lead with 10:44 left in the first half.
Ejim and Kane answered the Kansas State spurt with 28 first-half points while cutting the deficit to 39-34 at the break.
As the ''Big Three'' for the Cyclones, Ejim, Kane and Georges Niang all came in with scoring averages above 17 points per game in conference play.
Although two of the three lit up the Wildcats' defense, Kansas State coach Bruce Weber was happy with his team's effort.
''They had two special players in that arena with Ejim and Kane,'' Weber said. ''Both of them are up for being the top players in the league. They've had the big three all year and we did the job on Niang. Some of it was getting him in foul trouble, which helped.''
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.