Kansas, which has won or shared 12 of the 16 regular-season Big 12 titles since the league started, didn't score its first points until more than 7 minutes into the game. The Jayhawks finished with their fewest points in nearly six years.
The Jayhawks, who trailed by as many as 16 points, finally made a run a 17-4 spurt that got them within 44-40 on Jeff Withey's dunk with 6:49 left. Naadir Tharpe scored nine points in a 2-minute span with a 3-pointer before six consecutive free throws.
Tharpe had a chance to get it closer, but missed a 3-pointer on a break after rebounding a TCU miss. Adrick McKinney then slung a pass inside to Green for layup. Kansas guard Ben McLemore, the Big 12's top freshman scorer, missed an open 3-pointer before Green had a three-point play to stretch he lead back to 49-40.
TCU kept the Jayhawks in the game making only 5-of-12 free throws in a nearly 2-minute span before Elijah Johnson's 3-pointer got Kansas within 56-50 with just under a minute left. Johnson added another one from long range with 34 seconds left but that wasn't enough.
Nate Butler Lind had 10 points for TCU. Connell Crossland had eight points and 15 rebounds.
McLemore led Kansas with 15 points, while Withey had 12 points and Tharpe 11.
There was a record sellout crowd of 7,412 fans in the Daniel-Meyer Coliseum, a large portion of them loud Jayhawks fans cheering on their team coming off the loss Saturday that ended their nation's-best 18-game winning streak and a 33-game winning streak at Allen Fieldhouse.
But when this game ended, they were filing out of the arena while TCU students storm the court to celebrate the Frogs' first-ever win over a Top 5 team in 21 tries.
TCU, which had averaged just under 50 points a game since starting league play, scored the game's first eight points and led 22-13 at halftime.
Kansas shot a season-low 30 percent from the field (18 of 61) and had its lowest-scoring game since also scoring 55 in an NCAA tournament loss to UCLA on March 24, 2007.
Kansas already had six turnovers and missed its first four shots before finally scoring 7:17 into the game, on McLemore's bounce pass to Jamari Traylor for a layup that made it 8-2.
The Jayhawks didn't get closer before halftime, even after scoring seven points in a row over a 2½-minute span one point more than they scored the rest of the half.
Green's 3-pointer made it 20-6 before the only Kansas spurt of the half that could have been more if not for missed free throws.
McLemore made two free throws, and after Green missed another shot from long range, Kevin Young made a layup before Withey blocked a shot. But the Jayhawks then went to the free throw line on three consecutive possessions Kevin Young twice, and Travis Releford once and made only one of two freebies both times to get within 20-13.
Butler Lind's layup, with Withey still at the other end of the court after being knocked down without a foul, ended the Kansas spurt and was the last points before halftime.
Wednesday's Top 25 basketball scores
• TCU 62, No. 5 Kansas 55
• No. 7 Arizona 73, Stanford 66
• No. 11 Louisville 68, Rutgers 48
• No. 12 Michigan State 61, No. 18 Minnesota 50
• No. 14 Butler 77, St. Bonaventure 58
• Indiana State 76, No. 16 Creighton 57
• Providence 54, No. 17 Cincinnati 50
• No. 22 Oklahoma State 69, Baylor 67
• No. 24 Marquette 70, South Florida 47