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.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'