The Sooners (3-0, 1-0 Big 12) trailed 14-3 in the first quarter but then reeled off the next 28 points to take control of the Big 12 Conference opener for both schools.
Jones completed 35-of-48 throws, finishing with 448 yards and two interceptions. Broyles collected 12 passes for 154 yards for Oklahoma, which won its 38th straight home game.
Dominique Whaley contributed 150 total yards from scrimmage in the victory.
Missouri (2-2, 0-1) was led by James Franklin, who gained 291 aerial yards with one touchdown on 16-of-33 passing. He added 103 yards and two scores on the ground.