Chris Davis got the rally going with two outs and nobody on, singling to center off Angels closer Joe Smith (1-3, 4.50 ERA).
Mark Trumbo walked on a 3-2 pitch to bring up Wieters, who drove a 1-0 pitch from Smith over the fence in left-center.
Zach Britton pitched around a leadoff walk in the bottom of the ninth to record his 12th save for Baltimore (26-15).
Starter Kevin Gausman gave up a run on eight hits in six and two-thirds innings, striking out six and walking one.
LA starter Matt Shoemaker threw seven and a third shutout innings, striking out 12 and allowing three hits.