Marquez (1-1) allowed two runs on two hits in six innings, with two walks and six strikeouts. Chris Rusin allowed two hits in two scoreless innings of relief, and Adam Ottavino pitched a clean ninth with two strikeouts.
Story hit a three-run homer in the fourth and Blackmon added a solo shot in the eighth for the Rockies (10-8), who lead the National League with 26 homers. They have homered in seven of their past eight games, hitting a total of 14 in that stretch.
Colorado is 8-2 in its past 10 road games after dropping its first two of the season.
Steven Brault (2-1) gave up five runs and five hits in six innings, with two walks and one strikeout for Pittsburgh (11-5).
The Rockies scored twice in the first. DJ LeMahieu walked and scored on Chris Iannetta's double. Iannetta then came around on Blackmon's groundout to make it 2-0.
In the fourth, Story broke an 0-for-9 skid when he smacked a three-run shot to left for a 5-0 lead. Ian Desmond, who walked, and Carlos Gonzalez, who singled up the middle, scored on the blast.
Francisco Cervelli hit a one-out triple to right in the fifth for the Pirates' first hit. He scored on Colin Moran's sacrifice fly.
Pittsburgh made it 5-2 in the sixth when Gregory Polanco drew a two-out walk and scored on Starling Marte's triple to center.
Blackmon boosted Colorado's lead to 6-2 with a solo shot to left in the eighth off reliever Tyler Glasnow. All seven of Blackmon's home runs have come on the road. He is 5-for-12 with three homers and seven RBIs since he returned from a four-game absence because of a right quad injury.
The Pirates played without second baseman Josh Harrison, who was put on the disabled list earlier in the day because of a broken left hand suffered on a hit by pitch Sunday.
--Field Level Media