"He dropped it and we caught a break," said Yankees manager Joe Girardi. "'Tex' drove the ball a long way and the sun helped us out. We had some tough losses here. To get this one was important."
Brett Gardner and Derek Jeter singled to start the frame against Ervin Santana (11-11), then Scott Downs came on in relief. He fanned Curtis Granderson, but the Halos center fielder failed to catch Teixeira's hit, and both men scored to turn a 5-4 deficit into a 6-5 lead.
"I got a good jump on it and got back to the wall, but it just flashed in the sun," Bourjos explained on what led to his gaffe. "It's a play I have to make. It's hard to swallow. That was the turning point and it cost us the game."
New York opened up a 3 1/2 game lead over Boston in the AL East, with the Red Sox losing in Tampa earlier Sunday.
Freddy Garcia allowed seven hits and five runs with three walks and as many strikeouts in his five-inning outing.
Howie Kendrick and Bourjos each contributed a two-run homer for the Angels, whose three-game win streak was snapped. Los Angeles fell 2 1/2 games back of AL West-leading Texas after the Rangers topped Oakland.
Santana ultimately lasted six-plus frames, charged with eight hits and six runs, fanning eight but walking four.
Erick Aybar led off the first with a single and Kendrick followed with a two- run shot.
Chavez put New York on the board with a second-inning RBI single, then the Halos took a 3-1 edge in the home third when Garcia uncorked a wild pitch with two men in scoring position to plate Bobby Wilson.
Cano's one-out solo homer made it a one-run contest in the fourth, but Alberto Callaspo walked with one down and Bourjos launched a two-run shot to make it 5-2.
Jeter began the fifth with a single and Granderson pulled the Yanks within 5-4 when he followed with a two-run blast. The Angels had the bases loaded with one out in the home half but failed to extend their edge when Trumbo popped out and Callaspo grounded out.
LA also failed to score with runners on second and third in the home seventh.
Aybar singled with one out in the ninth, but Kendrick grounded into a game- ending double play.
"We shot ourselves in the foot all day. We left too many men on base and it came back to haunt us," noted Angels manager Mike Scioscia. "We didn't play the type of game to win."
The Yankees took five of nine from the Angels this season, and improved to 42-30 on the road overall...Rivera has notched eight seasons of at least 40 saves, and accomplished the feat for the second time in three years...The 41- year-old Panamanian reliever sits just two away from Trevor Hoffman's all-time saves mark...Granderson hit his 39th homer of the season, moving him one away from becoming the first Yankee to hit at least 40 in one season since Alex Rodriguez hit 54 in 2007...Aybar ended with four hits in a losing cause.