Johnson's score with 5:13 to go in the third quarter put the Chiefs up 28-20 and Kansas City (4-2) added a pair of late scores to win going away.
Matt Cassel was 13-of-18 passing for 193 yards, no interceptions and a pair of touchdowns, both of which went to Dwayne Bowe. The pair hooked up for a 53-yard scoring strike in the third quarter and again with 3:46 left in the game.
Thomas Jones carried the ball 20 times for 125 yards and a score and Jamaal Charles contributed 71 yards and a touchdown on 15 attempts for the Chiefs.
Todd Bouman completed 18-of-34 pass attempts for 222 yards, two TDs and two interceptions for Jacksonville (3-4).
Maurice Jones-Drew was held to 47 yards on the ground and 74 receiving yards in the setback.