The Rockies took advantage of a throwing error by D-backs starter Tyler Skaggs and a fielding error by center fielder Gerardo Parra on the same first-inning play to score two runs.
Colorado added another pair of runs in the second thanks to a two-out, two-run single by Josh Rutledge.
Rutledge, who figures to be Colorado's Opening Day second baseman had hits in his first three at-bats and drove in four runs. Tim Wheeler and Kent Matthes added solo homers.
Drew Pomeranz, who is battling to be the Rockies' No. 5 starter, allowed a pair of runs in two innings of work.
It was the debut of Rockies manager Walt Weiss, hired after Jim Tracy resigned in October. Weiss has insisted on an active offense and pitching aggressively down in the strike zone, and said he saw both.
"I thought our focus was on the right things -- there was an awareness," Weiss said. "It's Game 1 of Spring Training, so you don't want to get carried away. But the thing I liked was guys executed the things that we've really been hammering home."
Skaggs hurt his cause in the first when, with one out and a runner on first, he fielded a comebacker and fired over the head of shortstop Willie Bloomquist. The ball then scooted by Parra.
Reliever Heath Bell made his D-backs debut after coming over from the Marlins in an offseason trade. Bell allowed a pair of hits to begin his outing, but got a double play and then a strikeout to emerge from the inning unscathed.
Rockies up next: Left-hander Jeff Francis and righty Juan Nicasio, expected to be members of the 2013 rotation barring injury, will be the first to take their turns against the D-backs on Sunday. Behind them is well-traveled righty Miguel Batista and lefty Josh Outman, who are competing for middle-relief slots. Outman also figures in the starting picture.
Steve Gilbert is a reporter for MLB.com. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.