Kansas City took the final two outings of the three-game series. Boston has lost seven of its last eight.
Bruce Chen (1-4) gave up the three runs on seven hits over 6 2/3 to get the victory.
Jonathan Broxton allowed runners to reach second and third with one out in the ninth, but he retired Ryan Sweeney on a fly ball to shallow left and Mike Aviles on a grounder to short. It was Broxton's seventh save.