Chapman, a candidate to close games this year, had not allowed a run in his first four Spring Training appearances.
Downs, who is a reliever, got the start for the Astros after the club decided to throw Brett Oberholtzer in a Minor League game earlier in the day to avoid pending rain showers. The Astros followed Downs with a steady diet of relievers.
Left-hander Alex Wood started for the Braves and threw five scoreless innings, allowing two hits. He's yet to allow an earned run in four starts.
Up next: After taking advantage of Tuesday's off-day, the Braves will host the Yankees on Wednesday at 1:05 p.m. ET (listen on Gameday Audio). David Hale will be facing a Yankees lineup that is expected to include Brian McCann, who has not played at Disney since leaving the Braves via free agency in November. Hale is expected to be part of the four-man rotation the Braves plan to use during the regular season's first two weeks.
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.