Kim (3-2) allowed three hits and struck out five while working around three walks. Kim, who was traded to the Marlins on May 14 from Colorado, is 2-0 in three starts for Florida.
"Kim can be tough when he is in the strike zone like he was today. We as a team had a gameplan to make him throw strikes," Cubs catcher Michael Barrett said. "He came out pumping strikes and putting the pressure on us and got ahead of us, and his slider was working."
Kim struck out Derrek Lee to end the third inning with runners on first and third and pumped his fist as he left the mound.
"B.K. knows how it is. You give a team any chance to score and they do, it could get them on a roll. Once he got in a couple good innings, he did get into cruise control," said catcher Matt Treanor.
Sean Marshall (0-2), making his second start of the season, gave up an RBI single to Willingham in the first inning.
In the seventh inning, Abercrombie chased Marshall with a solo-shot to left-center. It was his second of the season.
Marshall lasted 6 1/3 innings, giving up three runs -- two earned -- and six hits. He struck out six and walked two.
Cubs reliever Scott Eyre allowed a leadoff double to Cabrera in the eighth inning. Cabrera scored on Wood's single.
The Cubs got all their runs in the ninth inning. Ryan Theriot hit an RBI single off Taylor Tankersley, and Cliff Floyd hit a broken-bat bloop single to center off Kevin Gregg that scored two. Gregg got the final three outs for his fifth save in five opportunities.
"The momentum was definitely on their side in that inning. To get out of there and preserve the victory, that's what it comes down to. It doesn't matter what it looks like. It's about getting those three outs," Gregg said.
Despite a $300 million spending spree in the offseason, the Cubs are 22-27 and have lost six of their last eight games, including a 2-1 loss to Dodgers in Los Angeles on Sunday.
"I think there is a little frustration because we lost a tough game (Sunday) and a little tired too because we came in late that night. It's tough, but that's not an excuse, we lost because they had very good pitching," said Alfonso Soriano.
- Marlins right-handers Josh Johnson, Henry Owens and Carlos Martinez are all scheduled to pitch in an extended spring training game on Tuesday in Jupiter, Fla.
- Kim snared a hard hit line drive off the bat of Ramirez in the first inning and doubled off Floyd.
- Theriot made an over-the-head basket catch on Hanley Ramirez's ball in the fifth inning. He made a nice bare-handed pickup and threw out Matt Treanor in the sixth.
- Since last the season, the Marlins have won five straight against the Cubs.