The Hooks, hosting Frisco, were leading, 12-4, when Backe exited the game. Backe, who did not issue a walk and recorded three strikeouts, had allowed one run through his first six frames.
Backe, who missed most of Spring Training with a strained left side, will likely make a fifth rehab start. The Astros have given no indication as to what they have in mind for the right-hander when he is ready to return to the team. Backe could take over the spot currently occupied by Felipe Paulino, who allowed seven earned runs over four innings in a loss to the Rockies on Tuesday night.
Paulino supplanted Russ Ortiz, who was moved to the bullpen to serve as a long reliever.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.