A strong effort from Angels (42-40) starter Dan Haren shut down the Nats' offense and didn't allow Washington to salvage a game in the three-game interleague series.
The only run scored in the game came on a Howie Kendrick double play ball in the fourth inning to deliver the 1-0 win for Los Angeles. Kendrick's ball scored Bobby Abreu, who reached base on Zimmermann's lone walk.
Jerry Hairston Jr. came out of the game in the fifth inning with a right hand contusion.
The Nationals will come home to finish out their first half of the season with a 10-game homestand beginning Friday night against the Pittsburgh Pirates.