Luis Valbuena hit a solo home run, Chris Coghlan smacked a tiebreaking two-run homer in the fifth and also scored on Anthony Rizzo's double in the first to give Jackson the offensive support.
Rizzo started a double play with a great leaping catch in the seventh and Arismendy Alcantara dazzled with his glove work as well in the second.
This was what the Cubs needed.
"It's good for the team," Jackson said. "We came in against a tough team coming off a [six]-game win streak. It's a high-style environment playing at Dodger Stadium. It's pretty loud and the fans are really into the game. It's good for us to come out and take victories like this and win series like this."
Jackson posted his first quality start since July 1 and picked up his first win since June 20. He struck out six over six innings.
"You can always use a positive outing to build on, and I think he gave us that," Cubs manager Rick Renteria said of Jackson. "He proved to himself that he can get beyond five innings, and be more efficient, which I thought he was. He used his pitches more effectively and kept us in the ballgame."
The Cubs were hoping Jackson could go deep after Saturday's 12-inning game, the third extra-inning contest in the last five games.
"The bullpen has been overworked, and a lot of that has been due to me not going deep in the games," said Jackson, who had not completed six innings in his four previous starts, and lasted four innings in his last outing, against the Rockies.
Coghlan was 2-for-3 with two walks, and doubled to lead off the game. He moved up on a passed ball, and scored one out later on Rizzo's bloop double to left.
The Dodgers loaded the bases with nobody out in the first on three straight hits, and tallied when Saturday's hero, Hanley Ramirez, grounded into a double play. Jackson then got Matt Kemp to ground out and end the inning. Jackson has given up 20 earned runs in the first inning in his 23 starts for a 7.83 ERA.
Jackson doubled to lead off the fifth and scored on Coghlan's home run, his sixth, for a 3-1 lead. Coghlan has reached safely in 27 of his 29 games, and had four home runs in that stretch.
"Any time you can go out there pretty much every day gives you an oportunity to produce," Coghlan said. "Honestly, it's just one of those things where you have to take pitch by pitch. I don't focus on the results. It's really just about in the moment what I can do and what I can control."
"He's come in really challenging himself," Renteria said of Coghlan. "He's a guy who wants to prove every day that's he's capable of being out there and he's got a good work ethic and has a good approach. He really plays the game with a lot of heart."
Alcantara followed Coghlan's homer with a single to chase Dodgers starter Josh Beckett, who has not pitched past the fifth inning in his last five starts.
"Josh has good stuff and he has the ability to strike out people," Dodgers catcher Drew Butera said. "He's done that for many years. Maybe the reason [he struggled] was that they took advantage of some mistakes."
Kemp homered in the sixth to pull the Dodgers within 1 at 3-2, but Brandon League walked the bases loaded in the Cubs eighth, and Chicago added runs on a groundout by John Baker and a two-run single by pinch-hitter Starlin Castro. Valbuena added a solo home run in the ninth.
The Dodgers' bullpen has been overworked, too.
"We had a long game last night," Los Angeles manager Don Mattingly said, when asked about League. "I don't want to make excuses for anybody but it's reality. Guys have to bounce back quick."
It's the first time the Cubs have won a series at Dodger Stadium since May 2-4, 2011, and will help make the off-day more pleasant. Renteria planned on staying in Los Angeles on Monday to catch up with family.
"We played a tough three-game series here," Renteria said. "Fortunately for us, we came out of here with two out of three. That's those guys in [the Cubs clubhouse]."