Jeter's throwing error in the eighth inning Wednesday night allowed the Royals to break a scoreless tie. Kansas City went on to win that game 3-0.
The Yankees, after going 10-0 against Kansas City in 1998, are 3-4 against the Royals this season.
The Royals won consecutive games at Yankee Stadium for the first time in since June 3-5, 1994. Since going 3-0 against New York in 1994, Kansas City was 4-18 before winning the last two games.
"Any time you can come to New York and win a series against the world champions, it feels good," Stein said.
The Royals wouldn't have had the chance to win if third baseman Joe Randa hadn't made a game-saving defensive play in the 10th. With runners on first and third and two outs, Randa made a diving, backhand stop of Bernie Williams' liner down the third-base line.
"I didn't even see the ball until Joe held it up in his glove," Royals manager Tony Muser said. "That's how hard it was hit."
"I cheated a bit in that direction before the pitch," Randa said. "Fortunately I moved enough to make the play."
Johnny Damon led off the 11th with a single off Grimsley (7-2). After Rey Sanchez sacrificed, Grimsley intentionally walked Carlos Beltran. The Royals loaded the bases when Jeter couldn't handle Mike Sweeney's grounder in the hole.
"Errors are going to happen to every player," Jeter said. "It just happened today in a bad situation."
Grimsley walked Jermaine Dye on four pitches, forcing in the go-ahead run. Randa then hit a sacrifice fly to center and Sweeney scored from second when Ricky Ledee's throw sailed into the Royals' dugout for another error.
The Yankees, who had just five hits, have scored just 12 runs in six games since beating Minnesota 14-2 last Friday in the opener of a seven-game homestand.
"We're just not getting it done," manager Joe Torre said. "There's a lot of hills and valleys, and right now we're in a bit of a valley."
The Yankees are hitting .169 in their last four games. Chili Davis, in an 0-for-13 stretch, and Joe Girardi, hitless in his last 17 at-bats, were given the day off. Davis pinch hit in the 11th and hit a game-ending groundout.
Scott Brosius led off for the fourth time this season despite entering in an 0-for-24 slump and went 1-for-5.
Stein kept the Royals in the game in his best start since a two-hitter last Aug. 19 for Oakland against the White Sox. He walked five batters in the first three innings, including the bases loaded in the third, before retiring 15 of his final 16 batters.
Stein matched David Cone, who allowed on run and five hits in seven innings. Cone has one win in six starts since pitching a perfect game against Montreal.
"There were times last year when we didn't score but we pitched well and times we didn't pitch well but scored," Cone said. "We haven't matched up as well this season. It makes you appreciate last year even more."
After three straight games that were scoreless through six innings, the Yankees were tied at 1 after six this time.
New York went ahead in the second when Ledee tripled and scored on Luis Sojo's single. Kansas City tied it in the third on Beltran's sacrifice fly.
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