Mazzaro (2-0) won for the second time in two starts since being called up from Class AAA Omaha Monday. The right-hander scattered four hits over six scoreless frames, allowing three walks and striking out three.
Kelvin Herrera and Greg Holland each contributed a shutout inning and Jonathan Broxton racked up his 13th save for the Royals, who took the rubber match of a three-game series at Kauffman Stadium.
Eric Hosmer belted a solo homer and Johnny Giavotella added an RBI single to provide Kansas City's offense.
Oakland's Tommy Milone (6-5) absorbed the loss, allowing a pair of runs on eight hits over seven innings.
The A's fell for the 10th time in 11 contests.