
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.
"He's had some good games that he's pitched and hasn't won. I think CC has done OK," Yankees manager Joe Girardi said. "We haven't scored a lot of runs for him."
Palmer spent seven seasons in the minors before making his big league debut with San Francisco last year, and he had an 11.74 ERA in two Triple-A starts this season before beating Detroit 10-5 in his Angels debut April 23.
Far from overpowering, the right-hander held the Yankees to one run after they totaled 36 during the winning streak.
"This afternoon was a case in point of him trusting the movement on his fastball," Angels manager Mike Scioscia said. "We knew it was in him to do this. Hopefully, it's the start of the change in a guy's career, because he has good stuff."
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 drive off the left-field fence on Sabathia's 119th pitch, and Mike Napoli's single off Jonathan Albaladejo made it 5-1.
"I've got to do a better job of keeping us in the game. I got two strikes and two outs and I just didn't make a pitch," Sabathia said. "I'm throwing the ball better than the first two or three starts. I'm throwing the ball better than I did at this time last year."
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, making his major league debut, 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.