Casey Paschall hit Carter with scoring strikes of 8 and 25 yards en route to a 24-for-35 for 335 passing performance.
Waymon James carried 12 times for 99 yards in TCU's (2-0, 1-0 Big 12) 10th consecutive victory dating back to last season.
Dayne Crist was 19-of-39 for 303 yards in the air for Kansas (1-2, 0-1). Andrew Turzilli caught three passes for 100 yards and Tony Pierson had 99 yards receiving and 35 yards on the ground.
Ron Doherty kicked a 37-yard field goal to give Kansas a 3-0 lead in the first quarter and added a 22-yarder in the second quarter to cut TCU's lead to 7-6.
Celebrity Families of 2014 [PHOTOS]