Rodriguez was hitless in three at-bats against De La Rosa, who gave up his 400th home run on May 8, 2005, while pitching for Milwaukee. A-Rod drew an intentional walk in the first, flied out leading off the fourth and was hit by a pitch in the fifth.
He grounded out against Zack Greinke in the eighth.
But thanks to a provision in baseball's rulebook, his 0-for-2 night might not matter.
On Friday, Rodriguez's 32nd birthday, he will be on deck when the Yankees resume a suspended game against the Orioles in the eighth inning. If he homers in the completion of the suspended game, it would count as being hit on June 28, when the contest began. That would make be home run No. 493 -- and his homer off Gil Meche on Wednesday night would become No. 500.
A-Rod would surpass Jimmie Foxx (32 years, 338 days) as the youngest player to reach 500 homers and would be the 22nd to reach the mark.
Rodriguez said he doubted the decision by Royals manager Buddy Bell to walk him was based on his pursuit of 500 homers.
"Buddy Bell's a great baseball man, and he wants to win a game," Rodriguez said. "He thought the best way to win the game was to put me on base. It had zero percent to do with 500 home runs. Zero."
New York went 0-for-12 with runners in scoring position -- hot-hitting Hideki Matsui stranded runners at second and third when he hit an inning-ending popup in the first, then left the bases loaded when he grounded out to end the fifth.
"We just couldn't get a hit when we needed to," manager Joe Torre said. "You know that's going to happen from time to time, and tonight was that time."
New York, which lost for only the third time in 14 games, dropped 7½ games back of AL East-leading Boston but remained 4½ games behind Cleveland, the AL wild-card leader. And after getting 84 hits in their five previous games, the Yankees were held to six.
"We had a couple of opportunities where we hit the ball well, but we hit it right to some people," said Derek Jeter, who was 0-for-4 and struck out twice. "They made some good defensive plays, and (De La Rosa) threw the ball well."
De La Rosa (8-10) won for the first time in three starts since July 8, allowing six hits and two walks in 5 1/3 innings with five strikeouts.
"We're never sure which Jorge is going to show up," Bell said. "Tonight he was outstanding. He got most of his pitches over, and he got some big outs early in the game."
Six of the Royals' seven extra-base hits came against Igawa (2-3), the Yankees' $46 million bust. He gave up five runs and seven hits in 5 2/3 innings, his ERA rising to 6.79. Igawa is winless since April 28, and with New York off on Monday -- and able to skip Igawa's next turn in the rotation -- it appears likely he will be sent back to the minors soon and replaced by 21-year-old rookie Phil Hughes, who has been impressive during a rehab assignment.
"He's missing some spots," Torre said of Igawa. "His stuff was good, but he still needs to command it. I still think he's going forward."
Kansas City went up 4-0 with four hits -- all for extra bases -- in the second inning.
It was the Royals' first inning with two three-base hits since Sept. 14, 2005, when Angel Berroa and Andres Blanco tripled in the sixth inning off Freddy Garcia of the Chicago White Sox.
The Royals' previous three-triple game was June 7, 2005, at San Francisco.
- C Jose Molina, acquired from the Angels on Saturday, was 2-for-4 in his Yankees debut. He doubled and singled in his first two at-bats, then grounded into an inning-ending double play in the sixth. ... New York has played four four-game series since the All-Star break and has gone 3-1 in all four.
- DeJesus was hit twice by pitches, one from Igawa and one from Henn. The Royals have been hit by pitches 61 times this season, most in the majors.
- It was the sixth time the Yankees were shut out, the first since June 30 against Oakland. Kansas City's only other shutout win was 1-0 at the Angels on June 27.
- Pena's eighth-inning walk was his first since May 5, ending a string of 244 plate appearances without one.