A 44-yard field-goal attempt by Louisville's Nate Smith on the final play bounced off the crossbar. Smith had also missed a 47-yard attempt with 2:36 left, and earlier failed on a 22-yard kick.
"The difference in that game was about three inches," Horned Frog Coach Gary Patterson said.
Texas Christian (9-0, 6-0) and No. 1 Oklahoma (9-0) are the only undefeated teams left in Division I-A.
Louisville (7-2, 3-2) got its last chance after Texas Christian was unable to run out the clock following Smith's 47-yard miss.
The Cardinals got the ball back at their 20 with 55 seconds left and no timeouts. Stefan LeFors completed passes of 10 and 19 yards to J.R. Russell, then on a fourth-and-15 play scrambled from pressure to complete a 29-yard pass to Robert Haskins to the Horned Frog 27 to set up Smith's attempt.