It was the fifth time Cook (5-1) stopped a Rockies' losing streak, and for the third straight start he ended a four-game losing streak. The Rockies are 6-1 when Cook starts and 6-18 in other games.
Taylor Buchholz pitched a perfect final 1 2-3 innings to pick up his first save of the season.
Andre Ethier homered for the Dodgers, who had their eight-game winning streak snapped. Derek Lowe (2-2) took the loss.
Cook mixed his sinker and fastball to record 16 groundouts, and at one point he recorded five straight. He scattered nine hits and struck out two. He left after giving up Juan Pierre's RBI single that made it 6-2.
Cook retired the first 10 batters and 13 of the first 14. He gave up a one-out solo homer to Ethier and a single to Blake DeWitt in the fifth, but he got Chin-lung Hu to hit into an inning-ending double play.
Pinch-hitter Delwyn Young led off the sixth with a single, but Cook got hot-hitting Rafael Furcal to ground into a double play.
The Rockies jumped on Lowe early. Omar Quintanilla doubled home Scott Podsednik, Holliday singled home Quintanilla, and then Lowe walked two to load the bases with no outs. He didn't record his first out until his 43rd pitch of the game, but he minimized the damage by allowing only one more run in the first.
Lowe settled down after that, and he retired 11 straight at one stretch before Cook singled to lead off the fifth. He gave up RBI singles to Holliday and Garrett Atkins and left after the fifth inning.
The Rockies cushioned their lead in the sixth when Podsednik singled to drive in Chris Iannetta to make it 6-1.
Notes: Torre said the Dodgers have had the eyes of slumping Andruw Jones examined several times. "They've checked out OK," Torre said. "We know his problems aren't physical ones and his hitting trouble isn't terminal."... Dodgers RHP Jason Schmidt (shoulder) will throw a simulated game in Los Angeles on Monday.... Furcal has reached base in all 31 games this year. He is three shy of tying Duke Snider 1955 record for the club's longest streak to start the season, according to Elias Sports Bureau.... Rockies INF Jonathan Herrera got his first career RBI in the eighth inning.