Kirk Hinrich scored 25 points for the Jayhawks (14-5, 4-1 Big 12), who avoided their third straight loss by rebounding from Saturday's disheartening 91-74 setback to top-ranked Arizona. The Jayhawks held a 20-point lead in that contest.
Against the Longhorns, they had to rally after trailing by as many as 12 points in the first half. In the victory, Kansas halted the Longhorns' eight-game winning streak.
"Losing to Arizona the way we did and to win this game against a great team gives us a lot more confidence in our team, and hopefully we can go win on the road," said guard Aaron Miles, who had 15 points and nine assists.
Kansas also posted its second straight thrilling victory over the Longhorns (13-3, 4-1). Last year in Austin, the Jayhawks walked away with a 110-103 overtime triumph as Drew Gooden scored 22 points after halftime.
"One of the best college games I have ever seen was when we played last year in Austin," said Kansas Coach Roy Williams. "I didn't think we would ever top that, but tonight may have been that."
One of the reasons was Collison, who had the most rebounds in one game for Kansas since Williams became coach 15 years ago. He grabbed a career-high 23 boards in getting his fifth double-double of the season.
Keith Langford chipped in 10 points for the Jayhawks, who avoided their first three-game losing streak since February 1994.
T.J. Ford had 25 points and 10 assists for the Longhorns, who had won their previous eight games by an average of 18.1 points.
"I kind of got a second wind in the second half and it really wasn't too bad fatigue-wise," said Collison, whose team was outrebounded, 45-32. "We just have to consistently bang with those guys."
"We just need to finish the last four minutes," said cat-quick Texas point guard T.J. Ford. "In all three of our losses, we have not been able to finish the last four minutes."
Ford was just 8-of-23 from the field as Texas shot 43 percent (30-of-70). The Jayhawks shot 47 percent (32-of-68) -- 55 percent (16-of-29) in the second half. Both teams went 20-of-28 from the free-throw line.