The game featured the return of New York shortstop Derek Jeter, who went 1-for-4 with a run scored and one RBI. Jeter was activated off the 60-day disabled list after recovering from a broken left ankle, an injury he suffered in the American League Championship Series last October.
Jeter, however, missed his final turn at bat Thursday due to what was described as an injured right quad.
Kansas City led 4-3 going into the fifth, when the Yankees loaded the bases with three walks and Overbay delivered a single to right to put New York ahead. Zoilo Almonte added an RBI single and Eduardo Nunez drove in Overbay for a 7-4 advantage.
Jeter knocked in Luis Cruz on a ground out in the sixth for the game's final run.
All eight of the New York runs came off Royals starter Ervin Santana (5-6), who gave up 10 hits and walked three.
Andy Pettitte (7-6) picked up the win despite allowing four runs over the first two innings. He didn't allow another run before leaving the game with two outs in the sixth.
Salvador Perez doubled in two runs and Lorenzo Cain added a sacrifice fly in the first inning for three Royals runs. After Jeter made the score 3-1, Alcides Escobar singled in David Lough to put Kansas City up 4-1 in the second.
Run-scoring hits from Austin Romine and Ichiro Suzuki in the bottom of the second pulled the Yankees within 4-3 until the New York rally in the fifth.