Jackson (8-15) overcame nine hits with the help of a pair of Cubs double plays en route to the victory. The right-hander didn't issue a walk and struck out four, tossing 68-of-98 pitches for strikes.
At the plate, Jackson belted his second career homer -- a solo shot in the seventh to cap the Cubs' scoring.
Welington Castillo (3-for-5) clouted two round-trippers while Donnie Murphy added a two-run shot en route to three RBI for Chicago, which rapped out 13 hits in the win -- the Cubs' second straight over the Reds.
Tony Cingrani (7-4) absorbed the loss after yielding two runs on three hits over 1 2/3 innings before leaving with back spasms.
Corky Miller got the only RBI for third-place Cincinnati, which fell four games behind National League Central-leading St. Louis.
The Reds still hold a six-game lead over Washington for the final NL wild card spot.