Carroll, who transferred from Vanderbilt before last season, had 20 points and a season-high 12 rebounds. He had 11 points on 4-for-6 shooting and 11 rebounds in the first half as Missouri (5-1) went on a 15-2 run to start the game and closed out the half on a 13-5 run. Missouri led 50-17 at halftime.
Hannah's point total was a season high on 8-for-12 shooting, including 3-for-6 from 3-point range.
Leo Lyons, who had his first career double-double in an 84-70 win over Maryland last week, finished with only eight points, but added a career-high six assists. Keon Lawrence added 10 points and six rebounds for Missouri.
The Leathernecks, which lost their 10th straight game against a Big 12 Conference foe dating back to 1993, shot just 38 percent from the field and committed 21 turnovers.
Missouri shot 53 percent from the field.
Sunday's game was the only one Missouri has in Columbia during a 22-day span. The Tigers last played at Mizzou Arena on Nov. 16 against Southern and won't play there again until Dec. 8 against Purdue.