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New York Yankees starting pitcher CC Sabathia looks at the ball after allowing a seventh-inning solo home run to Kansas City Royals designated hitter Billy Butler in a baseball game Tuesday, July 9, 2013, in New York.
NEW YORK—At this rate, CC Sabathia or any other Yankees pitcher would need to throw a shutout to win.

And even that might not be enough.

Cleanup man Travis Hafner and the rest of the New York hitters remained stuck in a collective slump Tuesday night, with James Shields and the Kansas City Royals posting a 3-1 win.

The Yankees have managed exactly one run in each of their last three games and lost them all—not since 2005 had they scored one run or fewer in three straight, STATS said.

Minus the likes of injured Derek Jeter, Curtis Granderson and Alex Rodriguez, the Yankees still put together a season-best six-game winning streak before this sudden drought.

"Obviously, getting back some of those guys that are hurt is going to be a big help. But I think that guys that are here can swing the bats better. And obviously myself," Hafner said.

"It looks like we need one of those games where you get some big knocks," he said.

Shields wiggled out of early trouble and got home run help from Billy Butler and David Lough.

Center fielder Lorenzo Cain contributed four nifty catches, defensive replacement Elliot Johnson ranged a long way for a grounder and Kansas City backed Shields (4-6) with a pair of double plays.

Fittingly, the game ended on a fine, twisting grab by another defensive sub, third baseman Mike Moustakas.

Sabathia (9-7) gave up seven hits in his second complete game. Yet the hitting slump left the Yankees with a three-game home losing streak for the first time since they dropped four in a row in late July 2012.

"The last three games we've had great pitching performances and we haven't been able to score runs and it's frustrating," Hafner said.

Lough led off the sixth inning with a tying home run and Butler opened the seventh with a go-ahead shot. Butler hit 29 homers last year and was an All-Star, but has slumped this season—he came into this series with six homers before connecting in the first two games.

Shields gave up three consecutive singles to start the game, and four hits overall in the first inning. He allowed just one more hit and left after the seventh.

"Any time you put four hits in an inning, you think you'll get more than one run," Yankees manager Joe Girardi said.

As for Sabathia and the Yankees' staff, "I think they are pitching pretty good. They're throwing pretty good ballgames. We're just not scoring runs for them," Girardi said.

Shields struck out five, walked two and retired his final 13 batters. Greg Holland worked the ninth for his 22nd save, and second in two nights.

The Royals are trying to win a series at Yankee Stadium for only the second time since the beginning of the 2000 season. Thanks to Shields and the bullpen, they're 2-0 in this four-game set.

Shields improved to 8-15 against the Yankees after overcoming a rocky start. Brett Gardner led off with a bunt single and Ichiro Suzuki and Robinson Cano also singled for a run.

Hafner struck out, but New York loaded the bases with one out. Shields fanned Lyle Overbay and then escaped when Cain ran down Eduardo Nunez's drive to deep right-center.

Shields didn't give up a hit after the second inning, sometimes pitching in rain and even hail.

Sabathia allowed only one hit until Lough homered. Butler's shot was the 20th homer yielded by Sabathia this season, second-most in the majors to the 21 off Kansas City's Jeremy Guthrie.

Doubles by Alcides Escobar and Eric Hosmer gave Kansas City an insurance run in the ninth.

NOTES: Gardner's streak of striking out ended at a team-record 16 games. He snapped an 0-for-16 rut with his bunt hit. ... Girardi said he hasn't ruled out rehabbing SS Derek Jeter from returning from the minors this weekend. ... Royals RHP Wade Davis (4-7, 5.42 ERA) starts Wednesday night vs. Yankees RHP Ivan Nova (3-2, 4.09). ... Cano's 32 hits off Shields are the third-most in the majors among an active hitter and pitcher, STATS said. Michael Cuddyer has 35 against Mark Buehrle, while Michael Young has 33 off John Lackey. If Manny Ramirez makes it back to the majors, his 36 off Andy Pettitte move to the top of the list. ... Rodriguez went 0 for 3 and struck out twice for Class-A Tampa.