The Horned Frogs (22-13) will play host to the Creighton Bluejays (20-14) on Tuesday, with the winner going to New York for the NIT semifinals at Madison Square Garden.
JD Miller added 15 points for the Horned Frogs, who led for all but 2:25 of the first half. Kendric Davis scored 12 points, including seven points during a crucial two-minute stretch when TCU took control in the second half.
James Palmer Jr., the Cornhuskers' leading scorer at 19.7 points per game, was 0-for-10 in the first half and didn't score until early in the second half. He finished with 19 points and passed Dave Hoppen as the single-season Nebraska scoring leader with 708 points.
Glynn Watson Jr. added 17 points, nine rebounds and six assists for the Cornhuskers (19-17). Tanner Borchardt scored a career-high 16 points and had 13 rebounds.
The Cornhuskers faced an uphill battle throughout the game and just couldn't catch the Horned Frogs, who seemed to have an answer every time Nebraska got close.
When Palmer heated up with two 3-pointers early in the second half, Bane answered with his own long-range jumper each time.
Nebraska's hopes were doomed when Isaiah Roby was ejected for a flagrant 2 foul after the Cornhuskers had come up with a defensive stop trailing just 57-49.
Roby, who had a career-high 28 points in Nebraska's first-round NIT win against Butler, was in foul trouble throughout and scored just four points.
Davis made the two free throws, and TCU made the Cornhuskers pay with Davis hitting a 3 on the ensuing possession to give the Horned Frogs a 62-49 lead.
Nebraska made one last run, when seldom-used Johnny Trueblood hit a 3-pointer and Palmer followed with a layup to get the Cornhuskers within eight at 62-54.
But consecutive layups by Davis and Bane pushed the lead back to 12 at 66-54 with about 10 minutes left in the game, and TCU cruised the rest of the way.
--Field Level Media