Akeem Wright added 12 points for the Wildcats (16-6, 5-2 Big 12), who have won six straight and own their first five-game conference winning streak since the Big 12 began play in 1996-97. The string started with an 85-81 victory over the Tigers on Jan. 13 in Columbia, Mo.
The 1989-90 Wildcats won five-straight Big Eight games. Kansas State's last six-game conference winning streak came in 1987-88.
Missouri (13-7, 2-5) was outrebounded 41-19 and had a two-game winning streak broken.
A 13-0 run, capped by Hoskins' three-point play with 4:51 left, gave the Wildcats a 65-58 lead. It was the fourth lead change in a streaky second half, after Kansas State led by three at the break.
Missouri cut the margin to two twice, the last time on Stefhon Hannah's basket with just over 3 minutes left that got the Tigers within 67-65, but could get no closer.
The Tigers were still within one possession, 71-68, when Keon Lawrence scored with 1 1/2 minutes to go, but the Wildcats scored six straight points over the next 50 seconds to put the game out of reach.
Hannah, a junior college transfer who went back on a commitment to the Wildcats because his mother wanted him to play for new Missouri coach Mike Anderson, heard chants of "Mama's boy" from Kansas State's student section almost every time he touched the ball.
If he heard them, it didn't show in his play. He hit six 3-pointers and led Missouri with 27 points.
Marshall Brown had 16 points and Lawrence finished with 15 for the Tigers.
Missouri got hot late in the first half and early in the second, making 10 straight shots after an 8-for-23 start. Hannah was 5-for-5 with three 3-pointers during that streak.
A 12-0 run that spanned halftime gave the Tigers a 41-36 lead, and they led 48-41 when Leo Lyons hit two free throws with 13:44 left.
The Wildcats responded with a 11-3 surge, going up 52-51 on Jermaine Maybank's steal and layup with 11:49 to go. A 7-0 run put the Tigers ahead 58-52 with 8 1/2 minutes remaining before Kansas State went on its game-winning tear.
Martin scored the first seven points in that run, including two free throws that put the Wildcats up for good, 59-58, with 6:15 to go.
The Tigers trailed by as many as 11 points early in the game but went on a 12-0 run to end the first half and open the second. Trailing by three at halftime, they scored the first eight points after the break for a 41-36 lead.
Kansas State jumped out to a 10-0 lead in just over three minutes and was up 16-5 with 14 minutes left in the first half, but Missouri closed the gap to 36-33 at the break.