Paul Shuey and Tom Martin fanned one batter apiece and Eric Gagne, who recorded his sixth save in as many games and 18th of the season, struck out two for the Dodgers. Los Angeles last won seven consecutive contests from June 26-July 4, 2001.
Despite striking out three times, the Rockies scored two unearned runs off Dreifort (4-3) in the top of the first, which began with a throwing error by Dodgers third baseman Adrian Beltre on a grounder by Jay Payton.
With two outs and runners on first and second, Mark Sweeney hit a double to shallow left field that delivered Payton. Left fielder Mike Kinkade hesitated on his throw to the infield, allowing Larry Walker to score.
Dreifort struck out four Rockies in the top of the second, allowing rookie starter Aaron Cook (1-4) to reach on a wild pitch on what have been the final out. Dreifort fanned Greg Norton to become the first Dodger to strike out four batters in a frame since Don Drysdale did it in 1965.
The Dodgers scored three runs -- the last on an RBI double by Dreifort -- in the bottom of the inning after errors by Rockies third baseman Norton and second baseman Brent Butler.
Colorado tied the contest in the top of the third on an run-scoring double by Sweeney, the Rockies' final hit.
Swim Week Miami Beach 2014 [PHOTOS]