Anthony Rizzo hit a two-run blast in the third inning and Starlin Castro contributed a solo shot in the fourth in helping the Cubs snap a three-game losing streak.
David DeJesus drove in three runs, one of them with an infield hit in the fourth and two more with a single in the sixth that gave Chicago a 6-0 cushion.
Jackson (7-11) was touched for eight hits, but did not walk a batter. He won for the fourth time in six starts.
The loss went to Wily Peralta (7-11), who allowed four runs on five hits in five innings.
There was a rain delay of just over an hour during the sixth inning.