The Wildcats (2-0) led 27-7 at halftime, showcasing a productive passing attack to augment the running of Thomas, who rushed for 234 yards last week against UCLA and has been touted as a Doak Walker Award candidate.
Coffman, who threw for only 66 yards a week ago, was 18 of 26 for 280 yards before sitting out the fourth quarter. With the undersized Bears (1-1) geared to stop the run, Coffman connected on scoring throws of 42 and 7 yards to Brodrick Smith, and 23 yards to Aubrey Quarles.
Missouri State is 1-24 all-time against FBS opponents.
Kansas State had 108 yards rushing in the opening half, with 45 of those coming on a touchdown run by Thomas with 11:50 left in the first quarter.
The Wildcats went to their bag of tricks to take a 13-0 lead with 9:45 left in the second quarter. Kicker Anthony Cantele, who earlier missed a 26-yard field goal, lined up for a 20-yarder. But holder Ryan Doerr took the ball on an option to the right side and pitched to a trailing Cantele for a 3-yard touchdown.
Cantele missed the extra point to take away some of the luster, but the Wildcats quickly made it 20-0 a couple of minutes later when Coffman found Smith for the 42-yard touchdown pass.
Missouri State finally got its offense in gear with a 66-yard touchdown pass from Cody Kirby to Jermaine Safford with 1:22 left in the first half. But Kansas State answered with the 23-yard score from Coffman to Quarles for a 27-7 halftime lead.
The Wildcats had 493 yards of total offense in tuning up for their Big 12 opener against Iowa State next Saturday.