Jake Bird (2-1) pitched an inning in relief to get the win and Justin Lawrence got the final four outs for his fifth save for Colorado.
Mookie Betts homered and Freddie Freeman and David Peralta had two hits each for Los Angeles.
The Rockies broke through in the second inning against starter Michael Grove when Harold Castro's two-out single brought home Nolan Jones to make it 1-0
Colorado padded the lead in the third. With one out, Tovar and Ryan McMahon singled, Elias Diaz struck out, Cron's bloop single brought home Tovar and Jones walked.
Grichuk lofted a two-run single to left-center to make it 4-0.
Grove allowed four runs on eight hits and struck out three in five innings.
The Dodgers rallied in the fourth inning off of Kyle Freeland. Will Smith and Miguel Vargas walked and Miguel Rojas singled to load the bases with one out. James Outman flew out to center but Freeland walked Jonny DeLuca on a 3-2 pitch to bring home a run
Yonny Hernandez followed with a two-run single up the middle to make it 4-3 and Betts hit the next pitch into the seats in left to cap the six-run inning. It was his 20th of the season.
Freeland allowed six runs on four hits, walked five and struck out seven in five innings.
The Rockies answered in the sixth. Grichuk singled, Jorge Alfaro (batting for Castro) doubled and Brenton Doyle was hit by a pitch to load the bases
Nick Robertson relieved Victor Gonzalez (2-3) and walked Jurickson Profar to make it 6-4. Tovar followed with a bases-clearing double and later scored on a single by Diaz.
Hernandez hit a sacrifice fly in the eighth, Betts walked and Freeman singled to drive in Peralta. Lawrence came on and walked Smith before striking out J.D. Martinez with the bases loaded to end the inning.
--Field Level Media