The Owls (3-4, 2-1 Conference USA) trailed 38-28 entering the fourth quarter but Greg Joseph kicked a field goal after missing two previous tries and Greg Howell scored his first touchdown of the season on 4-yard run with 2:18 left to tie the game.
Johnson, who also ran for a score, was 23-of-34 passing for 325 yards and three touchdowns, two to Whitehead, the conference's all-purpose yardage and receptions leader coming in. Whitehead had 125 yards receiving.
Brandon Doughty was 28 of 44 for 335 yards with three scores and an interception for the Hilltoppers (2-4, 0-3). Leon Allen ran for two scores for WKU, which tied a program record by scoring 30-plus points for the eighth straight game over two seasons.