Rafael Furcal fell a home run short of the cycle, going 3-for-5 with a single, a double and a triple, and Matt Kemp and Andre Ethier each homered to power the Dodgers' attack.
The 14 runs and 18 hits allowed were season highs for Cincinnati.
"I wouldn't want to face these guys right now," said Kuroda of his teammates.
Kuroda (2-0) allowed a season-high three earned runs on seven hits and struck out four in 5 2/3 innings. But while it was statistically his worst outing this season, he battled for the win.
"Kuroda had to work hard," said Dodgers manager Joe Torre. "You don't want to give up six runs. But I have found over the years that when you score 14 runs, I am a much smarter manager."
The Dodgers made it a difficult night for Reds starter Aaron Harang (0-3), who allowed seven runs (six earned) and 10 hits in 5 2/3 innings.
"We make pitchers make mistakes," said Kemp. "We have good at-bats, and we're hitting the ball well."
For the second consecutive night, the Reds grabbed an early lead.
Joey Votto hit a two-run home run and Scott Rolen followed with a solo shot to put the Reds ahead, 3-1, in the first inning.
"I didn't have my best stuff today," said Kuroda. "But as long as you pitch your game, this great lineup will help you win."
The Dodgers did just that.
A two-run double by Furcal and Ethier's solo homer in the second and third innings, respectively, helped them regain the lead.
The Reds tied the score in bizarre fashion in the fourth.
With the bases loaded and two outs, Harang hit a low line drive to right. Ethier appeared to make a diving catch to end the inning, and first-base umpire Tim McClelland ruled it as such.
Replays clearly showed the ball skipped into Ethier's glove. Reds manager Dusty Baker vehemently argued the call. The umpires conferred, then met with both managers near the third-base line after both teams had left the playing field.
The umpires eventually ruled it a hit, giving Harang an RBI single, which drove home Rolen to tie the score at 4.
Both teams were called back to the field, and Kuroda was allowed to toss a few warmup pitches before striking out Chris Dickerson to end the inning.
Following the fourth-inning drama, a bloop single by Manny Ramirez handed the one-run lead back to the Dodgers. Ramirez was 3-for-4 with two RBIs, giving him 1,800 for his career.
After his near-catch in the fourth, Ethier delivered a defensive gem in the fifth, when he fielded a single by Brandon Phillips and threw a dart to Casey Blake to retire Votto, who was attempting to go first to third.
It was all Los Angeles after that.
Furcal's RBI single in the sixth made the score 6-4. Then James Loney's two-run single with the bases loaded gave the Dodgers a 9-4 lead.
Kemp added his seventh home run -- a two-run blast -- in the seventh, which extended his hitting streak to 10 games.
"We are capable of having nights like this," said Torre. "There are times when we need to outhit our mistakes."
The Dodgers' bullpen enjoyed a relatively uneventful evening.
Four L.A. relievers combined for 3 1/3 scoreless innings in which they allowed just two hits.
Ronald Belisario, who was reinstated from the restricted list prior to the game, pitched a scoreless seventh inning.
The only concern for the Dodgers' bullpen on Wednesday night was the condition of reliever Jeff Weaver, who pitched to one batter in the eighth before leaving with back spasms.
"I felt a little jolt on my follow through," Weaver said. "I'm not too worried about it. Give it a couple days."