Wood (1-0) gave up a double to Clint Barnes in the third inning and two walks while striking out four in a six-inning start. He left the game with a 1-0 lead.
Chicago, which had only three hits on the day, led 3-0 in the ninth but Carlos Marmol gave up a single, a walk and back-to-back RBI singles to Andrew McCutchen and Gaby Sanchez that put the potential tying run on third.
The Cubs had just two hits through eight innings, using singles by Wood and Starlin Castro to produce a run in the third inning and beat James McDonald (0-1). Those were the only hits McDonald, who struck out four and walked two, allowed in seven innings.
Nate Schierholtz hit a two-run home run in the ninth for the other Chicago hit.