Hudson (1-0) held the Cubs to just one run on three hits, striking out seven with two walks as the Braves completed a three-game sweep of Chicago and improved to 5-1 on the season.
Pena's two-run single in the sixth inning broke a 1-1 tie and Dan Uggla belted a solo homer in the triumph.
Cubs starter Jeff Samardzija (1-1) fanned 13 but still took the loss, surrendering four runs on four hits while issuing four walks over 5 2/3 frames.
Chicago fell for the fourth time in five games.
Notable deaths of 2014 [PHOTOS]