The Astros broke open a 2-2 game with a four-run fourth and then hung on to even their three-game set with Washington at one victory apiece.
Bourn later added an RBI single while Clint Barmes socked a two-run homer and triggered the fourth-inning uprising with a run-scoring single for the Astros.
J.A. Happ (4-11) got the victory despite yielding five runs on seven hits in a 5 2/3-inning start. Four Houston relievers combined to hold the Nationals to one run over 2 1/3 frames and Mark Melancon picked up his eighth save.
Washington's Jordan Zimmermann (6-8) was rocked for six runs on seven hits before being pulled after five innings.
Michael Morse went 3-for-3, belted a two-run homer and scored twice while Jerry Hairston Jr. socked a two-run shot among his three hits for the Nationals.
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