Will Smith also homered as the Dodgers won for the eighth time in nine games. They began the afternoon two games behind San Francisco in the NL West.
The Reds lost their eighth straight series after starting the day two games in back of St. Louis for the second NL wild-card spot.
Kershaw (10-7) allowed one run and three hits, striking out eight without a walk. He pitched in Cincinnati for the first time since 2013.
The three-time NL Cy Young Award winner missed more than two months with inflammation in his left elbow, then returned Monday and threw 4 1/3 solid innings against Arizona.
The only Reds run against him came when Nick Castellanos doubled, advanced on a wild pitch and scored on Tyler Stephenson’s groundout in the fourth that made it 6-1.
Lux, who missed Friday’s game with a right forearm contusion, had three hits and drove in three runs. He hit a two-run triple Saturday in a 5-1 win.
Wade Miley (12-7) continued to struggle, allowing six runs and nine hits in a season-low three innings. The left-hander, who pitched a no-hitter on May 7 at Cleveland, has been roughed up for 19 hits and 12 runs, 11 earned, in 7 1-3 innings over his last two starts.
Pinch-hitter TJ Friedl, promoted by the Reds on Saturday, notched his first career hit and home run in the sixth. Friedl later singled and scored on Jonathan India’s double in the eighth.
Joey Votto lined a pinch-hit homer off Dodgers reliever Kenley Jansen in the ninth.
UP NEXT
Dodgers: After Monday’s off day, LHP Julio Urias (18-3) starts in the series opener on Tuesday at Colorado.
Reds: RHP Vladimir Gutirrez (9-6), Monday’s scheduled starter against the Pirates, allowed five hits, three walks and four runs in 3 2-3 innings of Cincinnati’s 5-4 loss at Pittsburgh on Wednesday.