In 2004, it took the miraculous scramble from Vince Young on 4th and 19 after a questionable pass interference call to set up the game-winning touchdown pass to Tony Jeffery and keep BCS hopes alive for the Longhorns, who went on to win another hard-fought game in the Rose Bowl against Michigan.
Last season, it took a fourth-down conversion from Case McCoy late in relief of an ineffective David Ash to emerge with a victory in a game that would have put head coach Mack Brown on the hot seat had Texas lost.
Despite those escape acts, the history of the Texas-Kansas series in Austin during the Mack Brown era is an entirely different story.
In four contests going back to 2001, the Longhorns have outscored Jayhawks 219-34 for an average margin of victory of 48 points -- nearly seven touchdowns per game. In 2001 and 2011, Texas shut out Kansas.
2011 -- Texas 43, Kansas 0
The beginning of the incredible two-game rushing stretch for the Longhorns, the rushing yards tell a stark tale of the game. Texas gained 441 yards on 72 rushes, throwing the ball only 21 times, while Kansas managed -2 yards on 20 attempts. Overall, the Longhorns picked up 35 first downs to only three for the Jayhawks, resulting in Texas holding the ball for just over 44 minutes in the game.
It's probably a good thing most of the country couldn't see the first Big 12 game to air on the Longhorn Network because it got ugly pretty quickly, even though Texas wasn't lighting up the scoreboard through most of the game.
2009 -- Texas 51, Kansas 20
The homecoming game for Kansas quarterback Todd Reesing, a Lake Travis product who started the run of quarterbacks that went on to include Garrett Gilbert, Michael Brewer, and Baker Mayfield, his return to the Austin area was supposed to be a little bit more triumphant.
Of course, the return to Texas for Missouri quarterback Chase Daniel hadn't gone much better the year before.
Two touchdowns and two field goals in the second quarter helped Texas get separation as Colt McCoy sliced up the Kansas secondary in his final home game, throwing his 396 yards on 9.4 yards per attempt. Jordan Shipley and Malcolm Williams both went over 100 receiving yards, while James Kirkendoll was the beneficiary of two touchdown passes.
Reesing managed to accrue 256 passing yards of his own, but the Kansas run game sputtered to only 47 net yards rushing and Reesing was under pressure the whole game, going down six times at the hands of Texas pass rushers.
2005 -- Texas 66, Kansas 14
The final home game for the seniors and quarterback Vince Young, though Texas fans didn't realize the latter fact at the time, it took less than 13 minutes of game time for the Horns to drop four touchdowns on the out-matched Jayhawks, the fourth courtesy of a 71-yard punt return from Aaron Ross.
Texas didn't let up in the second quarter, either, with 24 more points, and Kansas didn't move the scoreboards at DKR themselves until early in the third quarter, by which point the game had been out of hand for some time.
Overall, Mack Brown's squad out-gained Kansas 617 to 267, with Ramonce Taylor leading the way with 96 rushing yards and David Thomas collecting four passes for 76 yards and a touchdown.
2001 -- Texas 59, Kansas 0
Probably the ugliest of these four games, Texas raced out of the gate to score three touchdowns during the first quarter on drives that totaled barely more than three minutes combined.
In the end, Kansas had given up 606 yards to Texas, while gaining only 67 of their own, getting stuffed in the run game (33 carries for 27) and failing equally abysmally in the passing game (5-of-19 for 40 yards and two interceptions).
Running back Cedric Benson rumbled for 218 yards on 23 carries to do most of the heavy lifting for Texas, which also got over 100 yards receiving from Roy Williams, including a 68-yard touchdown pass from Chris Simms.
So, will be there another close game this year, the type of game that Brown is cautioning his players to avoid by turning on the tape of the near-decable in 2012?
History suggests not.