In the win, Yankees closer Mariano Rivera was touched for four straight hits in a ninth inning Kansas City rally that came up just short.
The Yankees completed a sweep of the three-game series and extended their winning streak to seven games, one shy of tying a season-high. They also stayed perfect against American League Central opponents at home, winning all 10 games.
Roger Clemens (12-7) continued his mastery of the Royals, improving his career record to 23-7 against them in 38 starts. It was his 305th career victory, tying him with Eddie Plank for 18th place on the all-time wins list.
The Royals rallied for four runs and seven hits in the ninth inning off Sterling Hitchcock and Mariano Rivera before Rivera struck out Desi Relaford to end the game for his 27th save.
Juan Rivera was called up from Triple-A Columbus earlier in the day.