Kershaw pitched eight stellar innings, and Ramirez hit a two-run homer off Cincinnati's Homer Bailey in a 2-1 victory over the Reds on Friday night.
Los Angeles maintained its half-game lead over Arizona in the NL West. The Dodgers are a major league-best 24-6 since June 21, when they were a season-worst 12 games out of first place.
Ramirez, acquired last year from the Marlins, is batting .387 with 11 homers and 33 RBIs in 47 games this season, despite two stints on the disabled list.
"Since I got here in this trade, everything changed -- even in my life," Ramirez said. "Being around these guys, it's unbelievable."
Kershaw (10-6) allowed a run and six hits, struck out eight and walked none, dropping his major league-best ERA to 1.96. The 2011 NL Cy Young Award winner is 5-1 with a 1.72 ERA over his last six starts after going 0-3 in six previous outings.
"They've got a great team over there, great lineup," Kershaw said of the Reds. "The key is to get these middle guys and not to give them any opportunities."
Kenley Jansen got three outs for his 13th save in 16 chances.
Bailey (5-10) lost his fourth straight since his no-hitter. He allowed two runs and seven hits in seven innings, struck out five and walked one.
"There's a reason why Kershaw has had the best ERA in the last three years, so it was out of my control," Bailey said. "The last three times out I've faced him, and Jeff Locke, and that dude from Atlanta (Mike Minor) -- he's got about a 2-something ERA. So what can you do?
"I'd like to face a guy with an ERA over 3.00. That would be great."
Kershaw and Bailey matches zeros until the sixth inning, when Adrian Gonzalez led off with a single, and Ramirez followed with a drive that just cleared the left field fence. It was his 11th homer of the season and 10th since coming off the disabled list on June 4.
"I made a pretty good pitch to Hanley there, a pitch that he had taken earlier in the game," Bailey said. "My numbers in the past against him had always been pretty good (1 for 12 coming in), but he's hot right now."
Ramirez also singled in the fourth inning and has reached base safely in 34 straight games, the second-longest active streak behind Joey Votto's 38-game run with the Reds.
"We knew we had the capability of doing this," Gonzalez said. "He's been swinging a hot bat. When he's going like this, we kind of all jump on his back. My job is to create opportunities for him."
Brandon Phillips led off the Reds' seventh with a double inside first base, and Jay Bruce singled him home two pitches later. Cincinnati got its fourth double of the game in the eighth when pinch-hitter Derrick Robinson tucked a grounder inside third base with one out, but Kershaw retired Shin-Soo Choo on a comebacker and then got Chris Heisey to pop out on his 118th and final pitch.
Until then, the Reds had gotten only one runner past second base. That was in the fourth, when Heisey led off with a double off the glove of center fielder Andre Ethier and advanced on Phillips' one-out grounder.
Kershaw escaped by striking out Bruce for the second straight time -- increasing Bruce's NL-worst strikeout total to 126.
"Both guys were dealing tonight, and it was a very good game. We just came out on the short end," Reds manager Dusty Baker said. "You know you're not going to get a lot of chances to score off Kershaw, but we did have some. We hit some balls hard off him. It was a tough one to lose."
NOTES: Kershaw's career ERA is 2.67, the lowest since 1920 by any pitcher with at least 100 starts and 1,000 innings. Whitey Ford and Sandy Koufax are second and third. ... Since the start of the 2010 season, Bruce leads left-handed batters with 41 home runs against lefty pitchers -- including seven this season. ... Reds C Corky Miller threw out Yasiel Puig trying to steal second base in the first inning. It was the fourth time in 10 attempts that the rookie has been unsuccessful, and the first time Miller has thrown out a runner this season. He is 1 for 8. ... Baker has an 89-108 managerial record against Los Angeles in his 20 combined seasons with the Reds, Giants and Cubs. ... The Dodgers, who dropped the series opener 5-2, haven't lost consecutive games since June 20-21 at San Diego. ... Puig was 0 for 4 with three strikeouts.