Montero and Soler both lofted balls into the left field basket off former Cub Edwin Jackson (2-2), sending Atlanta to its sixth straight loss.
Swisher homered from both sides of the plate in the same game for a record-tying 14th time to drive in four runs. He tied the Yankees’ Mark Teixeira, who homered right- and left-handed most recently in a game on July 31 against the White Sox.
Pedro Strop (2-6), the Cubs fourth reliever got the win.