Ogando (10-3) allowed just four hits and struck out five for the Rangers, who have five shutout wins in their last nine games.
Texas became the first MLB team to win 12 in a row since the Boston Red Sox did it in 2006.
Tyler Chatwood (5-6) took the loss, allowing three runs on seven hits and four walks over five innings. Michael Kohn coughed up another four runs in the final 1 1/3 innings.
Mark Trumbo went 2-for-3 for the Angels, including a double.
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