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: The Nationals return to Space Coast Stadium to play the Tigers for the third time in less than a week Thursday at 1:05 p.m. ET on Gameday Audio. Right-hander Stephen Strasburg, who has allowed just one run in nine spring innings and was named Washington's Opening Day starter Wednesday night, will get the nod.
Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time. He also could be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.