After an intentional walk to Nick Swisher loaded the bases with one out, Cabrera hit an RBI single on the first pitch from Justin Speier (0-1) for a 5-4 lead. Ramiro Pena followed with a two-run double for his first RBIs in the majors.
Johnny Damon and Mike Napoli became the latest hitters to launch shots over the inviting right-field wall at Yankee Stadium. The 28 home runs overall - 19 to right - are the most in the first seven games of a new park, one more than at Great American Ball Park in Cincinnati in 2003, the Elias Sports Bureau said.
Phil Coke (1-1) pitched a perfect eighth for the win. Mariano Rivera worked the ninth for his fifth save in six chances.
The loss left the Angels at 9-12 in April, ending their run of 15 straight months at .500 or better. That was longest active streak in the majors.
Mark Teixeira, who signed as a free agent with the Yankees despite the Angels' efforts to keep him, got booed after grounding into a double play in the seventh and striking out with the bases loaded to end the eighth.
Bobby Abreu, who wanted to re-sign with the Yankees but didn't get an offer, had a single, a stolen base and an error for the Angels.
Napoli's opposite-field drive off New York's A.J. Burnett in the second landed in an empty seat beyond the wall. Damon homered deep into the second deck in the third off Angels rookie Anthony Ortega.
This was the first home game for the Yankees since they cut some ticket prices and gave away free seats to fans who bought high-priced season plans. Still, the field-level sections right behind home plate were only half-full on a chilly evening.
The Angels held an early workout in the Bronx, taking batting practice and trying to get a feel for the new park. Chone Figgins got them off to a fast start, leading off the game with a triple and scoring on a groundout by Maicer Izturis.
After Napoli homered for a 2-1 lead, the Angels added another run in the second on a sacrifice fly by Erick Aybar - his bat cracked into two pieces, but the ball still carried to the warning track in right field.
Notes: New York's Robinson Cano extended his hitting streak to 17 games. ... Derek Jeter's 1,014th career RBI moved him past Bob Meusel for 10th place on the Yankees' list. ... RHP Ervin Santana (sprained elbow) will make a Triple-A rehab start Monday and RHP John Lackey (strained forearm) will pitch Tuesday. Both injured pitchers will need at least two minor league starts before rejoining the Angels, Scioscia said.
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