James Franklin completed his first 10 passes and ran for a 2-yard score for the Tigers (5-5, 3-4 Big 12), who beat Texas for the first time since 1997. Lawrence had 106 yards on 18 carries with a 35-yard score in the second quarter.
Texas (6-3, 3-3) entered with injury concerns at running back and was held to 76 yards rushing in only its third road game of the year. Missouri allowed only a chip-shot field goal for the game's first score and a safety off a blocked punt in the third quarter.
The Longhorns led by a combined 70-10 at halftime in the last two meetings but trailed 14-3 this time - Missouri's first lead in the series since a 17-16 edge in 1997.
The previous two weeks at home, Texas whipped Kansas and Texas Tech by a combined 95-20 and topped 400 yards rushing in both games. Leading rusher Malcolm Brown (toe) and Joe Bergeron (hamstring) got no carries and the depth chart got leaner after Fozzy Whitaker left with an apparent right knee injury while making a cut in the first quarter.
Josey was carted off with an apparent left knee injury in the third quarter. Texas coach Mack Brown came across the field to check on Josey, the Big 12's leading rusher from Angleton, Texas.
Josey also missed the last nine minutes of the first half after an apparent helmet-to-helmet hit.
Lawrence, who won the tailback job in fall drills but was shelved for three games early in the season by a broken fibula, stepped up with 79 yards on eight carries and a TD before intermission.
Missouri controlled play in the half even after fumbling away a scoring chance on its first drive when Emmnauel Acho stripped L'Damian Washington after a reception and Texas recovered at its own 12.
Franklin scored his 11th rushing touchdown on a 2-yard keeper to put Missouri ahead and Lawrence's 35-yard run made it 14-3 with 4:43 to go in the half.
Eric Waters' blocked punt set up Missouri at the 1 for its first score in the third quarter in four games, though the Tigers had to settle for a 19-yard field goal by Trey Barrow that made it 17-3.
Less than four minutes later, Leroy Scott's blocked punt out of the end zone gave Texas two points.