Texas A&M (23-9) led by as many as nine points early in the second half while the regular-season Big 12 champion Jayhawks (31-2) fouled and fumbled and committed turnover after turnover.
But the Aggies, who outplayed Kansas throughout the first half, ran into a sudden field goal drought that lasted more than 8 minutes and Kansas suddenly could hardly miss.
Sherron Collins had six of his 26 points in the big run that made Kansas 16-1 all-time against the Aggies and sent them into the finals against the winner between No. 9 Kansas State and No. 21 Baylor.
Donald Sloan, playing in his school-record 136th game, hit a jumper at the 8:52 mark that put the Aggies on top 57-56. But A&M didn't have another bucket until Sloan connected with 45.8 seconds left. Sloan led the Aggies with 24 points.
Marcus Morris, the Jayhawks' third-leading scorer, picked up his fourth foul with 11:58 to play and the Aggies holding a 51-48 lead. Less than a minute later, Cole Aldrich went to the bench with his third. With Morris and Aldrich both on the bench and A&M leading 55-51, Kansas coach Bill Self went with a small lineup with only one player over 6-foot-6.
Henry immediately drained a 3-pointer that ignited the game-turning run that gave Bill Self his 200th win as coach of the Jayhawks, one game after the storied program recorded all-time win No. 2,000.
Officials called a double technical foul on Markieff Morris and A&M's Bryan Davis after the teams began jawing at each other while struggling for the ball under the Aggies basket. Coaches went on to the court to separate everyone.
Texas A&M, a 59-54 loser at home to Kansas in February, also got 14 points from Khris Middleton and 12 from B.J. Holmes. Henry had 15 points and Markieff Morris had 10 while Cole Aldrich, plagued by turnovers in the first half had nine points and nine rebounds.