The Cowboys (7-1) scored 14 of the game's first 16 points.
After a dreadful first half, Missouri State (2-7) came out of the break hot and used a 10-0 run to claw back within 34-23 after Nathan Scheer's 3-pointer from the wing.
The Bears hit their first four shots and eight of their first 11 in the second half, but couldn't keep up the sharp shooting.
A turnover and three straight misses gave an opening for an 11-0 burst, and Cobbins' jumper with 8:09 left pushed the lead back to 53-31 and put it away.
The Bears came into the game shooting just 34 percent against Division I competition, losing all six of those games. In their previous two games, they were a combined 3 for 45 on 3-pointers.
They didn't fare any better against a Cowboys defense limiting opponents to just 36 percent shooting. Missouri State shot 33 percent from the field and made only three of its 18 tries from 3-point range.
Oklahoma State was just as cold from behind the arc, going 4 for 23, but dominated the glass 46-22.
The Cowboys were in control from the outset, scoring 13 straight points to go up 14-2 on Phil Forte's 3-pointer from the right wing with 14:14 left before halftime.
Forte, given a second chance after an offensive rebound by Cobbins, hit another 3 to spark an 11-0 surge to finish the first half and stretch Oklahoma State's advantage to 34-13.
Missouri State shot 6 for 28 (21 percent) from the field and got doubled up on the boards in the first half.
Oklahoma State has won all eight meetings in the series, including victories the past three seasons.
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Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.