Batista (1-0) struck out a career-best 11 batters in his first start since the 2004 season. The only runs he allowed came on a sixth-inning two-run home run by Matt Holliday.
By then the Diamondbacks had built a 10-0 lead with half the runs charged to Colorado starter Jeff Francis (0-1) and the rest to reliever Sun-Woo Kim. Those pitchers combined surrendered nine hits and eight walks.
Snyder, the first batter Kim faced, added a two-run home run in the fifth. The next inning Kim walked Jackson with the bases loaded and gave up a sacrifice fly before Snyder delivered a two-run double for the 10-0 lead.
Holliday's home run made the score 10-2 but Arizona got two more itself in the eighth with Snyder's sacrifice fly capping the rout.
The Rockies scored three times in the eighth off Arizona reliever Jason Grimsley.