Houston supported Cosart in the first against Washington right-hander Taylor Jordan. With one out, Jose Altuve reached base on an infield single, then stole second before going to third on a throwing error by Jordan. Altuve then scored on a groundout by Jason Castro.
The Nationals didn't collect their first hit until the sixth, when Anthony Rendon singled to right field off lefty Raul Valdes. Later in the inning, the Nationals loaded the bases with two outs, but Ryan Zimmerman flied out to right field.
Jordan, who is battling for the fifth spot in the rotation, pitched five solid innings, allowing the one run and striking out five.
The Astros added to their lead in the seventh when Jesus Guzman hit a Tyler Clippard pitch over the right-field wall.
In that same inning, Carlos Correa -- ranked as the Astros' top prospect by MLB.com -- left the game after he was hit on the left hand by Clippard. Correa felt fine after the game will have an X-ray on Thursday.
Up next: Right-hander Lucas Harrell, who allowed 12 hits and nine earned runs in 1 2/3 innings Saturday against the Tigers in Lakeland, Fla., starts against the Phillies at Osceola County Stadium at 12:05 p.m. CT on Thursday. Harrell, who is out of options, is fighting for one of the final rotation spots and could use a good outing to boost his chances. The game will air on MLB.TV and Gameday Audio.