Bray completed 14-of-25 passes with an interception.
He tossed an 8-yard scoring pass to Junior Hemingway with 5 seconds left in the first half to give the Chiefs a 13-6 lead at the intermission.
Bray then threw a 43-yarder to Josh Bellamy in the third quarter and a 9-yarder to Frankie Hammond in the fourth.
Green Bay's Vince Young was 14-of-30 for 144 yards, but the Packers managed just 218 yards of total offense while falling to 1-3 in the exhibition campaign. Kansas City finished 2-2.
The Chiefs open the regular season Sept. 8 by traveling to Jacksonville. The Packers will go to San Francisco on the same day in an early showdown between likely playoff contenders.
2014: The Year in Music [PHOTOS]