A 30-year-old rookie, Palmer (2-0) pitched three-hit ball for 6 1/3 innings before Los Angeles' struggling bullpen closed it out. Filling in for an Angels rotation decimated by injuries, he retired 14 straight batters between Hideki Matsui's RBI single in the first and Derek Jeter's leadoff double in the sixth.
"It's not about the guy that I was facing on the mound. He's not the guy I have to worry about," Palmer said. "I'm not surprising myself. I felt that I could always do it, just had to get the opportunity."
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."
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."
Jeter's throwing error helped the Angels tie it at 1 in the sixth on Morales' groundout. The next inning, Los Angeles solved Sabathia.
"Later in the game for some reason it just seemed like he started throwing a little more fastballs and guys just kind of -- we made the adjustment a little bit," Kendrick said. "We had a couple key hits and it seemed like once we got that first run in, guys started swinging the bats a little more."
Izturis took over at shortstop in the first inning after Erick Aybar was hit in the mouth by a deflected throw. X-rays were negative and Aybar might be available to play Sunday.
Angels OF Bobby Abreu sat out with a tight lower back. ... 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.