The Chiefs opened the scoring with an 11-play, 98-yard drive that culminated with a 5-yard pass from Alex Smith to Sean McGrath wth 14:52 left in the second quarter.
The Giants responded two plays later when Eli Manning hit Victor Cruz for a 69-yard score on a deep ball down the right sideline.
Ryan Succop gave Kansas City a 10-7 lead by making a 51-yard field goal with 1:55 left in the first half.
Josh Brown missed a 44-yard field goal in the final second of the half that would have tied the score.
Manning is 12-of-17 for 149 yards and one TD. Alex Smith of the Chiefs is 14-of-23 for 152 yards and one touchdown. Smith has hurt the Giants by running five times for 25 yards.
The Giants held Kansas City's Jamaal Charles to 14 yards rushing on seven carries in the first half.