Parra homered to lead off the first inning and drove home a pair of runs in the sixth with a double to left-center that increased the D-backs' lead to 3-0.
Randall Delgado started and pitched well for the D-backs. The right-hander, who is battling Patrick Corbin and Tyler Skaggs for the No. 5 spot in the Arizona rotation, tossed four shutout innings.
The only time Delgado found himself in trouble was the first inning when the Brewers had runners on second and third with one out.
Delgado settled down to strike out Carlos Gomez and Alex Gonzalez to end the threat.
Brewers starter Yovani Gallardo was sharp in his first outing since pitching for Mexico in the World Baseball Classic.
After allowing the leadoff homer to Parra, Gallardo retired the next 12 batters, including five by strikeout.
"It definitely felt good," Gallardo said. "Obviously, we didn't want to be back in camp this early, but it's a good feeling to be back with the guys and preparing for the season, getting in that routine."
Brewers reliever Jim Henderson had a rough night. The right-hander was charged with four runs in the sixth inning. He faced five batters, walked three and allowed a double while recording just one out.
Up Next: The D-backs will have their first off-day of the spring Thursday before returning to action Friday afternoon against the A's at Salt River Fields. Brandon McCarthy, who pitched for the A's the past two seasons before signing a free-agent deal with the D-backs this winter, will get the start. Another former A's pitcher, Brad Ziegler, is also scheduled to throw.
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.