The Texas team is also used to "protecting a lead". In the past, that lead might be 5 points. Now, the lead is at least 2 scores, usually more than 2 touchdowns.
What they need to learn is that, in that instance, the other side is going to come at you with everything they have! They're going to dig deep and bring maximum effort. Even with your big lead, that's a critical point. If you can withstand that "best effort" and keep their lead, then you've buried that team.
If that effort yields fruit, though, then the other side will go great blazes for the rest of the contest. Humans are funny that way.
In short, learn to close.