Cook pitched eight sharp innings and Jeff Baker drove in both Colorado runs with his first home run of the season, leading the Rockies to a 2-1 win on Wednesday.
Brian Fuentes pitched a perfect ninth for his eighth save in 11 chances, helping send the Dodgers to their 10th loss in 13 games. They are averaging 2.5 runs during that stretch -- which includes an 8-2 win Friday night in the opener of this three-game series.
"We haven't been swinging the bat, but that certainly takes nothing away from what Cook did," Dodgers manager Joe Torre said. "Yeah, it is frustrating. We're putting a great deal of pressure on our starters because of the way we haven't been swinging the bat. You hate to waste all this good pitching."
Cook (8-3) allowed a run and six hits, walked one and tied a season high with six strikeouts. The right-hander bounced back sharply from his previous outing last Friday, when he gave up seven runs and 10 hits in 6 1-3 innings against the Chicago Cubs in a no-decision at Wrigley Field. The Rockies lost that game 10-9 after blowing an 8-0 lead.
"I just wanted to forget those three bad innings I threw at the end of that last game," Cook said. "Today I just went out there with an aggressive attitude and was able to command my pitches from the first inning on. I had my sinker working and was able to use my slider off of it, so it turned out to be a good day for me."
The Dodgers, who lost 3-0 to Jeff Francis on Tuesday night, got their only run against Cook in the sixth inning. Chin-lung Hu reached on an infield single and scored from third on an infield single by Matt Kemp that ate up shortstop Omar Quintanilla, who was making his 14th start at short in place of the injured Troy Tulowitzki.
"They're an aggressive team. And if you make mistakes against them, they make you pay for it," Cook said. "I've just been executing pitches better against them and I didn't make quite as many mistakes today."
Clayton Kershaw (0-1) came up empty in his third attempt at his first major league win. The 20-year-old left-hander threw 104 pitches in five innings, allowing two runs and five hits with five strikeouts and four walks.
"He had really good stuff. He had a good fastball and a big league breaking ball. He's going to be good," Todd Helton said.
The Rockies wanted to get a good read on Kershaw's delivery and what he threw, so they let 16 of his 25 pitches in the first inning go by without swinging. Nine of them were called strikes.
"We were going to try and work counts as long as he was out there, try to elevate his pitch count and try to get him out of there by the fifth inning" manager Clint Hurdle said. "He threw strikes and we had to hit in some down counts, but that's what we committed to today. We wanted to get some good looks because he was a guy we haven't seen before."
Kershaw had no-decisions in his first two starts, giving up two runs in six innings against the Cardinals in his debut on May 25, then allowing four runs in 3 2-3 innings against the Mets last Friday. The Dodgers ended up winning both those games.
"He's still trying to control the situations, and himself," pitching coach Rick Honeycutt said. "That's what the game's about -- being able to make adjustments within a pitch or two. His stuff's obviously there. You just hate for one pitch to be the determining factor of a game. Unfortunately, that was the way it was today."
Baker gave Colorado a 2-0 lead in the second inning, capping a 10-pitch at-bat with a drive into the pavilion seats in left-center after Chris Iannetta lined a leadoff single off the glove of rookie third baseman Blake DeWitt.
"Baker was battling," Hurdle said. "To his credit, he probably swung at ball four and ball five and stayed in the count -- then he squared up and hit a homer. I just like to see him being aggressive, firing early and getting at least three swings every time he goes up there."
The Dodgers will have the 15th overall pick in Thursday's draft. Their last four first-round picks all were high school pitchers, including Kershaw and Chad Billingsley. ... Kershaw was the seventh overall pick in the 2006 draft. He was taken five spots after Colorado RHP Greg Reynolds, who is 0-3 in his first five big league starts. ... Dodgers 2B Jeff Kent, 11-for-19 lifetime against Cook, got the day off. ... Rockies 3B Garrett Atkins, who came in hitting a major league-best .514 against left-handed pitching, singled in three at-bats against Kershaw. ... Helton extended his hitting streak to 11 games with an infield single in the first inning. ... Chan Ho Park relieved Kershaw and struck out six in three innings, including his first four batters. ... Cook has gotten the decision in five of the Rockies' 10 road victories this season.