Reynolds hit a grand slam, Nolan Arenado and Trevor Story also homered, and Tyler Chatwood pitched five scoreless innings. The Rockies remained three games ahead of St. Louis and Milwaukee for the second NL wild-card spot.
Los Angeles still owns the best record in the majors at 92-51, but even that's becoming tenuous. Washington beat the Phillies on Sunday to cut LA's lead to four games.
The Dodgers have dropped nine in a row at Chavez Ravine for the first time in 30 years. Overall, Los Angeles has lost 15 of 16, including its longest drought since losing 10 straight in 1992.
Rich Hill (9-8) gave up two runs and four hits in five innings. Chatwood (7-12) allowed five hits and struck out five.
The Rockies won their sixth straight on the road for the first time since April 2015. They earned their first four-game sweep of the Dodgers since 2010, and the first in LA since 2007.
The Dodgers are just the fourth team in major league history to win 14 of 15 games and lose 14 of 15 in the same season, joining the 1914 Pirates, 1955 Phillies and 1959 Kansas City Athletics, according to the Elias Sports Bureau.
Los Angeles has 15 losses in the last 17 days. Before this drop-off, its previous 14 losses came over a span of 85 days, in which the team went 58-14 in that stretch.
The Dodgers last won on Sept. 1 when ace Clayton Kershaw pitched them to a 1-0 victory at San Diego.
They'll try to shake their stunning malaise when they hit the road Monday for a 10-game trip to San Francisco, first-place Washington and Philadelphia.
The Rockies took a 2-0 lead into the eighth, then broke it open with five runs. Reynolds hit his fifth career grand slam over the left-field wall off Walker Buehler, the Dodgers' prized prospect making his second appearance in the big leagues.
Buehler came on in the eighth and promptly gave up a single to DJ LeMahieuand walked Arenado. He struck out Story before walking Carlos Gonzalez to load the bases. Reynolds connected on a 3-2 pitch, sending many in the announced crowd of 50,161 heading to the exits.
Arenado homered leading off the third and Story hit a two-out, solo shot in the ninth.
Alex Verdugo hit his first major league homer leading off the bottom of the ninth to prevent the Dodgers from getting shut out.
Rockies: LH Kyle Freeland (11-10, 3.99 ERA) starts Monday at Arizona in the opener of a four-game series. His victories and ERA lead major league rookies. However, he's 0-3 with a 5.33 ERA in six starts since Aug. 4. He hasn't won since July 30 at Washington.