The Tigers (4-4, 1-3 Big 12 North) gained 267 yards on the ground and turned the game into a runaway with three third-quarter touchdowns.
Leon's five-yard run made it 21-6 with 8:46 left in the third and, after Kansas' Bill Whittemore connected with Byron Gasaway for a 20-yard touchdown just over three minutes later, the Tigers scored on their next two possessions.
Two plays after the Jayhawks (2-7, 0-5) got within 21-12, Smith raced in 75 yards on a quarterback draw, giving Missouri a 27-12 lead.
Following Smith's touchdown and blocked extra point, Darius Outlaw caught a 15-yard scoring pass with 1:01 left.
Smith extended Missouri's freshman rushing record to 798 yards and broke the 100-yard barrier for the fourth time this season.
Smith completed nine of 16 passes for 135 yards and moved from fifth to third on Missouri's single-season total yardage list with 2,365 total yards. He needs 181 yards to surpass Corby Jones' 1997 record.
Missouri senior wideout Justin Gage caught a 62-yard touchdown in the first quarter and finished with four receptions for 77 yards.