Kansas took a 17-14 lead on a 29-yard field goal by Nick Prolago with less than three minutes left in the game, but Texas drove 70 yards on its final drive for the go-ahead score.
On fourth and six from the UT 34, McCoy found wide receiver Jaxon Shipley for 18 yards to the KU 48. McCoy hit wide receiver Mike Davis for six yards to the KU 42 before connecting again for 39 yards down the left sideline to the KU 3.
Running back Johnathan Gray carried two yards to the KU 1, and on third and goal, McCoy hit Grant for the touchdown. Kansas had one last possession, but two Jayhawks passes fell incomplete.
Texas forced a Kansas punt on the game's first possession and found the end zone moments later after starting its drive at the KU 43. Gray ran 31 yards to the KU 12 and took the next carry to the KU 7. Running back Joe Bergeron carried four yards to the KU 3 before plunging in on the next play to give Texas a 7-0 lead.
Kansas evened the score early in the second quarter on a 15-yard touchdown run from Chris Matthews. The Jayhawks took a 14-7 lead with 7:16 left in the half when Tony Pierson found the end zone from 11 yards out.
Both teams went scoreless in the third quarter before Texas tied the game with 9:41 remaining in the game on an 11-yard touchdown run by wide receiver Marquise Goodwin.