New York overcame a 5-2 deficit in the eighth -- Teixeira tying the game with a three-run homer and the Yankees then scratching out the winning score after two were out.
Teixeira had five RBI overall, contributing a two-run blast in the third to give the Yankees a 2-1 lead.
Scott Downs, on the mound for the Angels to start the bottom of the eighth, gave up a leadoff double to Derek Jeter before walking Curtis Granderson. Teixeira followed with his 17th homer of the season.
Downs (1-1) then retired the next two batters, but walked Nick Swisher.
Kevin Jepsen replaced Downs and faced pinch-hitter Raul Ibanez. Dewayne Wise, who ran for Swisher, stole second and Ibanez was walked intentionally. Russell Martin was next and his single to right scored Wise with the winning run.
The comeback made a winner out of Chad Qualls (2-1), who recorded the final two outs of the eighth inning in relief of starter Hiroki Kuroda. Rafael Soriano gave up a one-out single in the ninth on the way to his 21st save.