Harrell (11-11) handcuffed Chicago on a pair of hits while issuing only one walk and striking out seven.
Jose Valez and Francisco Rodriguez teamed up for 1 2/3 scoreless relief frames and Wesley Wright notched the final five outs for his first save of the season.
Fernando Martinez homered while Matt Dominguez and Scott Moore added RBI as the Astros won the first game of a season-ending three-game series.
Jason Berken (0-3) was tagged with the loss for the Cubs, yielding two runs on four hits over 4 2/3 frames.
Swim Week Miami Beach 2014 [PHOTOS]