Jake Heaps threw for 279 yards and a touchdown for the Jayhawks (2-1), who hadn't defeated another FBS team since beating Northern Illinois on Sept. 10, 2011. James Sims added 78 yards rushing, while Tony Pierson had nine catches for 82 yards.
Louisiana Tech (1-3) was poised to score the go-ahead touchdown with when it marched to the Kansas 18 with 1:33 left. Kenneth Dixon got the carry and was fighting for extra yardage when the ball popped loose inside the 5-yard line, and the Jayhawks' Keon Stowers recovered it.
The Bulldogs also lost a fumble inside the 5 earlier in the fourth quarter.
That gave Kansas the ball back with just enough time for Heaps to get the Jayhawks in position for Wyman, who was cut from the team last year, to kick the game-winning field goal.
Dixon finished with 129 yards rushing for the Bulldogs. Ryan Higgins threw for 289 yards and a touchdown in place of starter Scotty Young, who missed the game with bruised ribs.
The first half was ugly on just about every account. The teams combined to miss three field-goal attempts, the Jayhawks twice failed to convert on fourth down, and an egregious interception by Heaps eventually led to the only touchdown of the half.
Heaps appeared to have some miscommunication with his wide receiver and threw a pass over the middle right to Bulldogs safety Thomas McDonald. That gave Louisiana Tech the ball near midfield, and it took 10 plays before Higgins hit Hunter Lee on an 8-yard fade pass for the score.
It was the third time in three games that Kansas fell behind early.
The Jayhawks tried to answer with a solid drive that fizzled once it made it to the Louisiana Tech 6. Wyman missed a 28-yard field goal wide right.
Louisiana Tech squandered a chance to build on its lead when Kyle Fischer missed a 37-yard field goal so badly it looked as if the ball deflated in midair. Wyman later tacked on a 39-yard kick to get the Jayhawks within 7-3, and Fischer's 40-yarder just before halftime also missed.
Fischer finally ended a 0-for-4 slide on field goals that dated to last week's loss to Tulane when he hit from 39 yards early in the third quarter. That gave the Bulldogs a 10-3 lead, though it seemed much greater than a touchdown the way their defense was playing.
Kansas had to start from inside its own 10-yard line on three straight possessions in the second half. The third one ended when Heaps was picked off by Daniel Cobb on a batted pass, giving the Bulldogs the ball at the 29-yard line. Higgins promptly scrambled 27 yards, but a video review showed he lost possession before stepping out of bounds and the result was a touchback.
The overturned call - Higgins was ruled out initially - proved to be pivotal.
Heaps hit on three consecutive passes, including a 20-yard throw to Christian Matthews to convert a third-and-3 situation. He finished off the drive by hitting Jimmay Mundine, who picked up a key block from Matthews and then pirouetted into the end zone to knot the game 10-all.