Tampa Bay roughed up Hiroki Kuroda in tightening its grip on an AL wild-card spot with its fifth straight win. Matt Joyce had a leadoff homer as the Rays jumped ahead 3-0 in the first and David DeJesus had two RBI doubles.
Tampa Bay has a one-game lead over Cleveland for the top wild card with five to play. Texas is two behind the Rays. Kansas City played later.
The Yankees trail the Indians, who won 5-4, by five games -- and also are behind the Rangers and Royals. The Yankees would be eliminated Wednesday if Cleveland wins or they lose.
"This is not a good feeling," manager Joe Girardi said. "It hurts."
Moore (16-4) gave up only three hits but threw three wild pitches to up his AL-leading total to 16 and walked six. Jamey Wright and Jake Odorizzi, who earned his first career save with three innings, finished the four-hitter that ensured New York could not pass the Rays in the standings.
"It was a little bit challenging out there just to kind of get you know some good sequences going where I was having a solid release point," Moore said. "I feel like I was trying to get way too aggressive with put away pitches, like I was trying to miss the bat."
The defeat gave the Yankees 75 losses for the first time since they lost 86 games in 1992.
The Rays got right to work against Kuroda (11-13), tagging him for three more first-inning runs.
Maddon put Joyce in the top spot with hopes of getting him going. In a 3-for-41 slump coming in, Joyce connected on a 1-1 pitch for the Rays seventh leadoff homer of the season. Wil Myers followed with a single and DeJesus drove him in with a double to right field. Evan Longoria's sacrifice fly capped the inning.
"You set the tone right from the start," Joyce said. "Obviously Wil and David coming up behind me and not just settling for a couple of runs. But you know we kept attacking them, kept being aggressive and kept scoring and that's what it's going to take."
Kuroda has yielded 23 of his 77 runs this season in the first inning.
After that, the biggest mystery for the eerily quiet late-season crowd of 43,407 was if the Mariano Rivera bobblehead dolls would arrive before the end of the game. The figurines were delayed by train and truck trouble in a cross-country journey, and the Yankees were forced to give out vouchers to the first 18,000 fans entitled to one of the promotional gifts in tribute to the retiring closer.
Alas, the bobbleheads arrived in the third inning.
The Yankees were 0 for 10 with runners in scoring position overall.
"We all know the situation, but you can't win ballgames when you can't put runs on the board," said Vernon Wells, who was 0 for 4. "You give their pitcher credit but we had opportunities and didn't come through."
Kuroda settled down after the first and held Tampa Bay hitless until the sixth, when James Loney doubled with the bases loaded for two runs.
Kuroda extended his winless skid to eight starts, matching a career worst first done in 2008 with the Dodgers. The 38-year-old right-hander was having one of his best seasons until he was hit hard Aug. 17 at Boston. This time, he allowed five runs and five hits in 5 2/3 innings.
"I'm really disappointed I'm not contributing to the team," Kuroda said through a translator.
Rays SS Yunel Escobar left with a sore left ankle. "He's not awful but I'm not sure about tomorrow yet," Maddon said. C Jose Lobaton has a bruised right elbow. "He's fine I think he should be fine," Maddon said. ... Yankees RHP Phil Hughes will take LHP CC Sabathia's spot in the Yankees' rotation on Wednesday. Sabathia sustained a Grade 2 strain in his left hamstring in his start Friday, and was shut down for the last week of season Monday. ... Maddon had no report on OF Desmond Jennings (tight left hamstring). Jennings played catch before the game but did not run. ... The bases had plates on the sides with "Mariano Rivera" and "42."