Grichuk's double came against Justin Garza (0-1) and broke a 4-4 tie. Coco Montes and Nolan Jones scored on the play.
The Rockies extended their lead to 7-4 when Jurickson Profar drove in Grichuk with a sacrifice fly
Rafael Devers hit his second two-run home run of the game to make it 7-6 in the bottom of the 10th, but the Red Sox stranded the tying run on second base
Daniel Bard (3-0) picked up the win -- his second victory in as many games -- by pitching a scoreless ninth inning. Pierce Johnson recorded the final two outs to earn his 12th save.
The Rockies built a 4-0 lead by scoring three runs in the third and one in the fourth. Elias Diaz hit a three-run double that scored Profar, Ezequiel Tovar and Ryan McMahon in the third. Grichuk singled, took second on a wild pitch and scored on Brenton Doyle's double in the fourth
Devers sliced Colorado's lead in half when he homered in the bottom of the fourth. Justin Turner, who reached on a single, also scored on the play, which made it a 4-2 game.
The Red Sox climbed within a run after Turner's RBI single scored Pablo Reyes in the fifth, and tied the game at 4-4 when Adam Duvall scored on Christian Arroyo's sacrifice fly in the sixth
Boston's Kutter Crawford pitched the first four innings and gave up four runs on five hits. He struck out five and walked three.
Colorado starter Chase Anderson exited the mound after 4 1/3 innings. He allowed three runs on five hits, struck out six and walked one.
--Field Level Media