Ricardo Ratliffe had 12 points and eight rebounds, while Phil Pressey and Michael Dixon contributed 12 points apiece for the Tigers (15-1, 2-1 Big 12), who rebounded from a 75-59 loss to Kansas State on Saturday. Steve Moore and Kim English both had 10 points in the victory.
Scott Christopherson led the Cyclones (12-4, 2-1) with 19 points and five rebounds, while Chris Allen netted 17. Royce White finished with 16 points and six boards for Iowa State, which had its seven-game winning streak halted.
"They made the effort plays all night," Iowa State head coach Fred Hoiberg said. "We just weren't tough enough. We just could not get any loose balls or rebounds and it was too easy for them in the post"
After a tight first half in which Iowa State led by as many as six and Missouri led by as many as three, the Cyclones held a 38-36 lead heading into the second half of play.
Iowa State shot 48 percent from the floor in the opening 20 minutes and 8- of-12 from three-point range, while Missouri shot 46 percent from the floor.
The game remained close throughout most of the second half, with nether team leading by more than five through the first six-plus minutes. Then, Missouri began to pull away slightly.
Leading 57-55 with 7:32 to play, the Tigers used a 9-3 burst to take a 66-58 lead with five minutes to go in regulation.
A three-pointer by Chris Babb with just over two minutes remaining cut the deficit to 68-64, but Ratliffe answered with a jumper on Missouri's next possession to push the lead back to 70-64.
A pair of free throws by Allen with 1:03 to go pulled the Cyclones within four, but Ratliffe came through again for the Tigers on their next touch as he put home a layup with 32 seconds to play, putting Missouri ahead 72-66.
Marcus Denmon made four from the stripe in the last 22 seconds to secure the win for Missouri.
"It was a great win for us. I thought our guys really found a way to grind out a road win," Missouri head coach Frank Haith said.
These two teams have met every year since 1909 with the exception of two seasons (1915, 1927). The Tigers hold a 148-84 series advantage and have won each of the last eight meetings...Missouri shot 52 percent from the floor and 23 percent from beyond the arc, while Iowa State shot 44 percent from the field and 52 percent (12-of-23) from three-point range...The Tigers got the better of the play inside, outscoring Iowa State 20-8 in the paint...Denmon finished with six points and four rebounds.