Wood (9-11) scattered six hits, didn't issue a walk and struck out seven, tossing 70-of-100 pitches for strikes in the gem.
Pedro Strop contributed a scoreless eighth inning and Kevin Gregg wrapped up the win with his 31st save as the Cubs took the opener of a three-game series.
Reds starter Bronson Arroyo (13-11) yielded just the two runs on seven hits in a seven-inning performance. He didn't allow a walk and struck out six.
Cincinnati, who came into the contest tied for second place in the National League Central, fell two games behind division-leading St. Louis with the loss.
The Reds hold a seven-game lead for an NL wild card spot.
Texas principal bans speaking Spanish, stirs controversy
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie