It was the Horned Frogs' (5-1) second win in a row after a surprise loss at home to Lipscomb knocked them out of the AP Top 25. They had been ranked 18th.
Larry Austin Jr. led the Chippewas (6-2) with 19 points and five assists.
Guard Jaylen Fisher was back in the starting lineup for TCU, having missed the final 16 games of his sophomore season with a torn meniscus in his right knee. He missed three more games this season after arthroscopic knee surgery in September.
Fisher, who averaged 12.3 points a year ago, finished with 14 points and six rebounds.
"Jaylen brings really good ball movement as well as player movement, and we can't underestimate that," TCU coach Jamie Dixon said. "That's opening it up for a lot of guys, including (Bane).
"We need Jaylen out there. There's no question he makes us better."
Robinson entered the night tied for first in the nation with 9.0 assists per game. His 12 on Friday put him in a tie for fourth place on TCU's career assists list.
TCU, which leads the Big 12 in assists, finished with 29, one game after recording 31 against Eastern Michigan.
"Those are ridiculously high numbers, but this is a team that can do those kinds of things," Dixon said. "Alex is great at finding guys and passing up open ones to get even better shots.
"(Fisher and Robinson) are really good together. They make each other better."
Bane staked the Horned Frogs to a 20-point halftime lead, with 18 points and seven rebounds before the break. During an 11-0 stretch that broke open the game, Banes scored eight, including two 3-pointers. He made 4-of-5 from beyond the arc in the first half.
"They can beat you in so many ways, and they really don't seem to have any weaknesses that you can expose," Central Michigan coach Keno Davis said. "We were hoping to stay away from any big runs like they had in the first half, but they were able to get to the basket and make their 3's."
CMU: The Chippewas picked up a win and a loss on their two-game road swing through Texas, which included an 81-65 win over Sam Houston State.
TCU: The Horned Frogs entered the game leading the Big 12 in field goal percentage at 50.9 percent. They shot 55 percent from the field against Central Michigan, scoring 46 points in the paint.
CMU: The Chippewas play Tuesday on the road at Youngstown State and then return to Mount Pleasant, Michigan, for a four-game home stand to close out 2018.
TCU: The Horned Frogs travel about 40 miles east for their first road game of the season, on Wednesday at SMU in Dallas. Next Friday, they travel to Los Angeles to play USC in the Basketball Hall of Fame Classic.