Pomeranz needed 72 pitches to make it through three innings. He gave up five hits and one walk, but the Braves couldn't score against him despite having two runners on in each inning.
"One big key to the game tonight was the fact Drew was fighting his command but he got a couple big outs when he needed to get them which actually kept them off the board," Rockies manager Jim Tracy said. "From there the guys that picked him up were terrific."
Carlos Torres (4-1), who took over after Pomeranz lasted only three innings, threw three scoreless innings. He allowed three hits with no walks and three strikeouts.
Pomeranz said patient approaches by Atlanta's hitters helped send his pitch count soaring.
"I felt I was in a lot of 0-2 and 1-2 counts and trying to throw good pitches to get them out," Pomeranz said. "They were being very patient. ... Pitches add up pretty fast."
Gonzalez broke a scoreless tie with a one-out homer off Tommy Hanson in the fourth that landed deep into the center field seats.
Gonzalez, who had two hits, has 22 homers -- including only two since July 23.
"We are without some significant people," Tracy said. "For him to continue to do the job that he's doing, I think you have to tip your cap to him. When I say hitting hasn't been easy, I think the opposition is well aware of the damage he can do. There are times they are not going to afford him a whole lot of opportunity."
Pacheco, who had two hits and drove in two runs, led off the fifth with his fourth homer on an 0-2 pitch for a 2-0 lead.
Hanson (12-8) said he shouldn't have given Pacheco a pitch to hit, but he said Gonzalez hit a good pitch.
"The 0-2 pitch needed to be buried," Hanson said.
"The one to Gonzalez, not so much. He got me. He's a good hitter and ... that's not one of those situations where I'm going to beat myself up over it."
Hanson allowed two runs and five hits, including the two homers, in 5 2/3 innings. He has lost three straight starts.
The Braves' best scoring chance came in the sixth, when Martin Prado singled and moved to third on Jason Heyward's single with one out. Heyward took off for second when David Ross struck out. Prado then broke from third base and was thrown out at the plate by second baseman D.J. LeMahieu.
Sloppy play by the Braves helped the Rockies add to their lead. The Braves, who began the night leading the NL in fielding, had three errors.
Colorado took advantage of a fielding error by first baseman Freddie Freeman on LeMahieu's grounder and wild pitches by Moylan and Luis Avilan to score two unearned runs in the seventh. Dexter Fowler's single drove in LeMahieu. Torres, who walked, scored on a wild pitch by Avilan.
The Rockies added two runs in the eighth. Colvin doubled off Chad Durbin and scored on Pacheco's single. LeMahieu singled to right, and Heyward's throw to third base skipped past Chipper Jones for an error. Durbin's wild throw to the plate, for another error, allowed Pacheco to score.
"That seventh and eighth inning got away from us a little bit," Braves manager Fredi Gonzalez said. "A couple wild pitches. We're better than that defensively."
Dan Uggla grounded out to third base as a pinch-hitter in the seventh inning in his first at-bat since Gonzalez told him he lost his starting job at second base.
Uggla remained in the game, and Prado moved from second base to shortstop.
Pacheco has a 13-game hitting streak. ... Braves RHP Kris Medlen was the NL Player of the Month and then posted on Twitter he just learned his unborn child will be a boy. Medlen (7-1) was 4-0 with a 0.50 ERA in five August starts. ... Gonzalez said the team doesn't plan to recall RHP Jair Jurrjens, who was sent to Triple-A Gwinnett on Aug. 1 because of a right groin strain. Jurrjens was 3-4 with a 6.89 ERA in 11 games with Atlanta this season. ... Gonzalez said C Brian McCann, who hasn't played since he was given a pain-relieving shot in his sore right shoulder after Saturday's game, could return Wednesday. ... Braves LHP Mike Minor will face Rockies RHP Alex White when the four-game series continues on Wednesday. Minor gave up 10 hits and eight runs in five innings at Colorado on May 5.