Palmer (2-0) pitched three-hit ball for 6 1-3 innings before Los Angeles' struggling bullpen closed it out. The right-hander, filling in for an Angels rotation decimated by injuries, retired 14 straight batters between Hideki Matsui's RBI single in the first and Derek Jeter's leadoff double in the sixth.
It was another disappointing outing for Sabathia (1-3), the free-agent prize who signed a $161 million, seven-year contract in the offseason. The big lefty is winless in his last four starts since beating Kansas City on April 11.
The 30-year-old Palmer spent seven seasons in the minors before making his big league debut with San Francisco last season. Far from overpowering, he held the Yankees to one run after they totaled 36 during the winning streak.
Palmer had an 11.74 ERA in two Triple-A starts this year before beating Detroit 10-5 in his Angels debut April 23.
The bottom two batters in Los Angeles' lineup, Brandon Wood and injury sub Maicer Izturis, singled to start the seventh.
Two outs later, Howie Kendrick snapped a 1-all tie when he grounded an RBI infield single up the middle. Hunter followed with a two-run double off the left-field fence on Sabathia's 119th pitch, and Mike Napoli's first-pitch single off Jonathan Albaladejo made it 5-1.
Jose Arredondo escaped a bases-loaded jam in the bottom half by retiring Jeter on a comebacker, and Morales homered to right-center leading off the eighth against Jose Veras.
Juan Rivera added an RBI single in the ninth, and another run scored on an error by right fielder Melky Cabrera.
Fernando Rodriguez gave up Jorge Posada's two-run shot in the ninth. It was the 31st home run at the new Yankee Stadium - at least one in each of the nine games. The record for the first nine games at a major league ballpark is 33 at Kansas City's Municipal Stadium in 1955, according to the Elias Sports Bureau.
New York got another run when right fielder Gary Matthews Jr.
dropped Jeter's two-out fly for a three-base error, but Jason Bulger struck out Johnny Damon to end it.
Jeter's throwing error from shortstop helped the Angels tie it at 1 in the sixth on Morales' groundout.
Palmer hit Jeter on the left elbow with his second pitch. One out later, Jeter stole second as Napoli bounced a throw that caromed off Jeter's helmet and hit slick-fielding shortstop Erick Aybar in the jaw.
Aybar stayed face down in the dirt for a few moments before walking off the field with the help of a trainer. He was taken to see Yankees team dentist Dr. Scott Levy.
X-rays were negative. Aybar received several sutures in his upper lip and might be available for Sunday's game.
Izturis replaced Aybar at shortstop for the Angels, who already have seven players - including six pitchers - on the disabled list.
Notes: Angels OF Bobby Abreu sat out with a tight lower back. ...
Angels manager Mike Scioscia said LHP Darren Oliver (strained left triceps) should be activated from the disabled list Monday. ...
Yankees OF Nick Swisher sat out while receiving treatment on his bruised right elbow. ... New York's Robinson Cano went 0 for 4, ending his 18-game hitting streak.
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