His Atlanta Braves look to even this weekend set at Wrigley Field, where they hope their bats finally get untracked.
Minor (2-5, 4.54 ERA) is 0-3 with a 4.86 ERA in nine starts since beating Milwaukee on May 19. He took a step in the right direction Monday by allowing two runs and two hits in seven innings in a 4-3, 11-inning loss to the New York Mets.
The left-hander has posted a 3.56 ERA in winning all five starts against Chicago (40-52), limiting Starlin Castro to three hits in 15 at-bats and Anthony Rizzo to a single in six. He has 37 strikeouts to four walks in those games, and has been aided by a 9.49 run-support average.
The Braves (50-43) could be in position to give Minor similar support as they face Jackson (5-9, 5.05), who is 0-3 with a 3.96 ERA in six starts against them.
Jackson gave up three runs in six innings in a 5-2 loss at Atlanta on May 11, holding Freeman hitless in three at-bats while Upton missed the contest with a back injury.
Freeman entered the season 7 for 11 with two homers against the right-hander while Upton is 6 for 11 with one homer and two doubles.
Jackson owns a 3.86 home ERA compared to his 6.05 road mark that matches teammate Travis Wood for the NL's worst.
The home team has taken all four meetings. Chicago won 5-4 on Friday after being swept in a three-game set in May.
Atlanta has totaled 15 runs with no homers while losing five of six after averaging 5.6 runs during a season-high nine-game win streak that preceded this stretch.
Jordan Schafer stole three bases Friday and B.J. Upton got the day off despite going 6 for 18 in his last four games.
"I'm happy with those guys at the top of the order," manager Fredi Gonzalez said. "Now we need to keep the line moving, and we will."
Chicago blew a one-run lead in the ninth inning Friday when Hector Rondon allowed Christian Bethancourt's two-out RBI single.
The game seemed destined for extra innings before Arismendy Alcantara singled with two outs in the bottom half, stole second and scored on Justin Ruggiano's single.
Alcantara made his third straight start since his big-league debut Wednesday in Cincinnati. He's 5 for 13.
"This young man actually just has the energy and the desire to be out there," manager Rick Renteria said. "He's very composed, he's got a lot of poise to him right now for being here for the first time."
Alcantara has been starting at second base for Darwin Barney, who returned Friday from paternity leave. Renteria said that Alcantara could see action in center field if Barney starts at second.
The Braves are hitting .214 in day games for baseball's second-worst average ahead of San Diego. The Cubs are one of the majors' worst hitting teams at home at .233.