Correia (11-9) baffled Chicago on just two hits, walking one and striking out six in a contest delayed nearly 4 hours by rain.
Cubs starter Travis Wood (6-12) hit Clint Barmes with a pitch to lead off the third inning and Brock Holt followed with a single. One out later, Marte ripped a pitch into the left-field corner, chasing home both runners.
Jose Tabata then added a run-scoring double to wrap up the scoring.
Wood allowed three runs on four hits in a 5 2/3-inning stint for the Cubs.