Schwarber sent a deep drive into the left-center field bleachers on a 3-2 pitch from Burke Badenhop (1-4). The blast scored Dexter Fowler, who had singled with two outs.
Bryant drove in two runs for Chicago, which had lost five of six but is still in good shape for its first playoff berth since 2008. The Cubs entered play Tuesday 5 1-2 games ahead of San Francisco for the NL's second wild card spot.
Hector Rondon picked up his 25th save in 29 tries. Fernando Rodney (6-5) allowed Eugenio Suarez's homer in the seventh that gave the Reds a short-lived 4-3 lead but won his first game since the Cubs acquired him from Seattle on Aug. 27.
