Shields (4-6) yielded a run on four hits in the first, but then settled down to blank New York on just one more hit the rest of way. The right-hander gave up two walks and struck out five en route to the victory.
Tim Collins tossed a scoreless eighth and Greg Holland turned in a 1-2-3 ninth for his 22nd save as Kansas City notched a second straight win in its four-game series at Yankee Stadium.
CC Sabathia (9-7) took the loss, yielding three runs on seven innings in a complete-game effort. He walked two and struck out three.
Robinson Cano drove in the only run for New York, which dropped a third consecutive game overall.