Chris Taylor homered, tripled and drove in three runs and AJ Pollock also hit a home run for the NL West leaders.
Kershaw (6-2) threw just 86 pitches -- 59 for strikes -- while striking out six and not walking a batter.
"It feels good to pitch well here and get a win. It's a tough place, you just try and do your best here," said Kershaw, who improved to 11-5 in his career at Coors Field. "I felt like my curveball was a little bit better than my last start, which was encouraging. Just keep building, felt good."
Taylor hit a two-run triple in the first and then homered leading off the fourth, his seventh of the season, to put the Dodgers ahead 3-1 and give Kershaw all the runs he needed.
"He's fun to play behind. As an infielder, I appreciate it," Taylor said. "I think it's more predictable what the hitters are going to do against him because he always hits his spots. He gets a lot of rollovers from righties. I love pitchers who work ahead and throw strikes and keep you in the game. I appreciate that as a shortstop. I think our whole defense appreciates that."
Pollock hit his 12th home run of the season in the seventh to give LA a major league-high 100 this season. The Dodgers scored two more on a wild pitch by reliever Mychal Givens and a throwing error on a pickoff attempt that allowed Mookie Betts to score from second base.
"The throw to second base on an attempted pickoff was not wise," Rockies manager Bud Black said.
Colorado got its only run in the first when Tapia legged out a double, stole third and came home on a groundout.
"Tap was hard out of the box right from the get-go, good hard turn and recognized there was a really good chance to get to second and went for it," Black said. "It was Tap out of the box, making a good read.
Chi Chi Gonzalez (0-2) went five innings.
Dodgers: Manager Dave Roberts said RHP Walker Buehler threw a simulated game on Saturday and could start Thursday against Oakland. Buehler last pitched on Sept. 8 and has been dealing with a blister issue. "I think he'll throw again at the secondary site when we're on the road," Roberts said. "I think that he'll do one more simulated -- probably six innings and 90 pitches -- and then he'll make his last start of the season with us and be ready for the postseason."
DAVIS ERA OVER
After a pair of rough seasons, Colorado has parted ways with closer Wade Davis by designating him for assignment Saturday. Davis was signed to a three-year deal before the 2018 season and led the NL that season with a franchise-record 43 saves. He struggled last year and was 0-1 with a 20.77 ERA in five appearances this year after missing most of the season with a right shoulder strain.
"He was a great presence on our team and a great mentor for a lot of our younger pitchers. He was one of our leaders," Black said. "The shoulder woes started happening and he just really couldn't recover totally."
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