Starlin Castro also added an RBI double for the last-place Cubs, who won just for the third time in 13 games.
Jackson (3-3) had his best outing for the Cubs since signing a four-year, $52 million deal before the 2013 season. The right-hander allowed four hits and walked one. He struck out the side in the first and struck out Elian Herrera to end the fifth for his 10th strikeout. He finished his outing by striking out Jeff Bianchi on 95 mph fastball.
Hector Rondon pitched a perfect ninth for his fourth save in four opportunities.
Milwaukee starter Matt Garza (2-4) was tagged for three runs on four hits. In his second straight start that he allowed three runs in the first inning