Ryan Succop booted four field goals and Jackie Battle ran for a game-clinching, 1-yard TD run with 5 minutes left, assuring the Packers (13-1) would suffer their first loss in 20 games dating back to last season.
The Chiefs defense sacked Aaron Rodgers four times and limited him to 235 passing yards on 17-of-35 efficiency.
The Packers' 19-game winning streak was the second-longest in NFL history.
They fell for first time since Dec. 19, 2010, at New England.
Members of Congress to keep receiving porn magazine
Rosie O'Donnell unveils nearly 50-pound weight loss