Randle, who ran for 138 yards on 14 carries, scored three times on the ground in the second half and caught a 16-yard scoring pass from Brandon Weeden in the first half to lead the undefeated Cowboys (7-0, 4-0 Big 12) to their ninth consecutive road win.
Weeden threw three touchdown passes in the contest and finished 33-of-49 for 338 yards.
Missouri (3-4, 1-3) quarterback James Franklin had a tougher time of it. Franklin was 14-of-27 for 184 yards and was intercepted three times and lost a fumble.
Franklin ran in one touchdown and connected with T.J. Moe late in the second quarter on a 34-yard TD pass that cut the Cowboys' lead to 24-17 at the end of the half.
The second half was all Oklahoma State. Randle ran for scores of 16 and 59 yards in the third quarter and added a 12-yard TD run with 45 seconds left in the game.