Brown picked off Robert Griffin III deep in Baylor territory with less than 5 minutes left and four plays later Anthony Cantele kicked a 31-yard, game-winning field goal for the Wildcats (4-0, 1-0 Big 12).
Quarterback Collin Klein amassed 114 yards on 25 carries and went 13-of-27 for 146 yards and two touchdowns through the air for KSU, which won its conference opener in an upset.
Griffin, meanwhile, surrendered his first interception of the year on the crucial play. He ended with 346 yards on 23-of-31 passing for the Bears (3-1, 0-1).
Kendall Wright made nine grabs for 201 yards and three touchdowns in Baylor's loss.