Turner accumulated 104 yards and Jerious Norwood added 75 on 11 carries for Atlanta (2-1).
Falcons quarterback Matt Ryan threw 18 passes, completing 12 for 192 yards and a touchdown. Roddy White caught five throws for 119 yards and a score, and Chris Houston intercepted a pass and ran for a touchdown.
Kansas City quarterback Tyler Thigpen made his first NFL start and was intercepted three times. Atlanta racked up 17 points following the interceptions..
Thigpen finished with 14 completions for 128 yards and a touchdown.
Larry Johnson gained 121 yards and scored a touchdown in 24 carries for the Chiefs (0-3).