The Longhorns (19-12) have taken out the Tigers (13-18) in the first round each of the last four years. UT moves on to face Texas A&M in the quarterfinals.
Kathleen Nash led the Longhorns with 16 points, including four 3-pointers. RaeShara Brown had 18 points for Missouri.
The Tigers trimmed a 15-point deficit to nine with a 6-0 run to start the second half but couldn't sustain the momentum.
UT set the tone by shooting 59.4 percent in the first half while racing to a 48-33 lead. The blistering pace was fueled by Nash, Yvonne Anderson and Ashley Gayle, who combined to hit 12 of 17 shots. The Longhorns committed just four turnovers in the first half.