Grant stepped into the end zone and grabbed a 1-yard toss from Casey McCoy with 12 seconds left on the clock, capping a 70-yard Texas scoring drive.
The Longhorns (6-2, 3-2 Big 12) outscored the Jayhawks (1-7, 0-5) 14-3 in the second half but trailed 17-14 with 2:28 to play after Nick Prolago kicked a 29-yard field goal for Kansas.
The TD pass to Grant was one of only seven passes thrown by McCoy, who replaced David Ash and completed five throws for 68 yards. Ash went 8-for-16 for 63 yards and was intercepted twice.
Johnathan Gray ran for 111 yards, almost half of Texas' total of 211 rushing yards.
Kansas freshman quarterback Michael Cummings was 3-for-9 for 39 yards.
James Sims carried the ball 28 times for 176 yards and Christian Matthews and Tony Pierson each ran for a TD.
Notable deaths of 2014 [PHOTOS]