Tampa Bay wound up the day with a two-game division edge over Boston, which split a doubleheader with Toronto. The Rays franchise has never won a doubleheader in 13 tries.
Derek Jeter collected three hits in each game and Wilson Betemit hit a solo homer in the nightcap for New York, which opened its final homestand at Yankee Stadium.
Four New York relievers combined to throw 5 2-3 innings after Sidney Ponson struggled in the makeup of Friday night's rainout.
Damaso Marte (1-3) pitched a scoreless seventh, Joba Chamberlain worked the eighth and Mariano Rivera got three outs for his 34th save in 35 opportunities.
Rivera allowed pinch-hitter Evan Longoria's RBI single with two outs before Justin Ruggiano grounded out. Longoria returned to action in the opener after missing more than a month with a broken wrist, and hit a bases-loaded single.
Ben Zobrist hit his second career grand slam, but committed a crucial error for Tampa Bay.
Zobrist's fourth-inning slam made it 4-1. A pair of errors let New York take the lead in the seventh.
After led off with a single, Bobby Abreu followed an easy grounder to shortstop that Zobrist threw into right field. Jeter scored when Gabe Gross had trouble picking up the ball.
J.P. Howell (6-1) then struck out Alex Rodriguez, but Nady hit a 3-2 pitch from Grant Balfour into center field to give New York a 5-4 lead.
Abreu added an RBI single in the eighth for the Yankees.
New York is almost certain to miss the playoffs for the first time since 1993. The Yankees are eight games behind wild card-leading Boston with 14 games remaining.
Shields (13-8) allowed five hits, walked none and struck out six to earn his first win in eight career starts against New York. He also improved to 1-3 with a 6.35 ERA in five games at Yankee Stadium, which is being replaced by a new showplace across the street.
"It's good to end on a good note," Shields said.
Mike Mussina (17-9) threw five shaky innings and first baseman Jason Giambi committed an unseemly error that led to another run.
"We gave them two or three extra outs and they capitalized on that," manager Joe Girardi said. "When you do that it's tough on the pitcher."
A sellout crowd of 54,088 was mostly silent as New York sputtered against Shields, who is 2-1 with a 2.43 ERA in his last four starts. There was an occasional smattering of boos but the fans seemed mostly resigned to their team's poor play.
Shields set a career best for wins and also became the first Tampa Bay pitcher with two seasons of more than 200 innings.
Ruggiano went 3-for-4 with two RBIs.
Longoria went 2-for-5 in his first game since he was hit by J.J.
Putz's pitch on Aug. 7. His two-run single off Mussina in the fifth inning gave Tampa Bay a 5-0 lead.
Longoria also made an outstanding diving stop and strong throw on Nady's two-out grounder to third base with two on in the sixth.
"It's like riding a bike," he cracked.
The Rays pushed across two runs in the sixth. Zobrist hit a sacrifice fly and Ruggiano scored when Giambi threw Carlos Pena's grounder over the head of reliever Dan Giese covering first.
