But Roenicke showed some frustration after the Diamondbacks scored three eighth-inning runs off reliever Brandon Kintzler to beat the Brewers 7-5.
"We need Kintzler to throw the ball well. He makes some good pitches and then, all of a sudden, he gets a pitch up," Roenicke said.
Aaron Hill hit a two-run home run in the eighth inning after Miguel Montero had a tying single.
"The bullpen has been really good. I know the last few games they haven't been quite as good, but they've pitched great," Roenicke said. "That's why we've won so many ballgames. I need to show confidence in them because I think they are really good."
A dejected Kintzler said his pitching mechanics aren't "as sound as I would hope."
"I left two pitches up. I just need to get more consistent. I feel terrible for letting the team down in that situation," he said.
Hill had the game-changing hit a night after going 4-for-4 with a pair of RBI singles. He's batting .472 (17-for-36) with four home runs and 11 RBIs in eight career games at Miller Park.
Evan Marshall (1-0) pitched 1 1-3 innings of scoreless relief in his major league debut for the victory. Addison Reed pitched a scoreless ninth inning to record his ninth save in 10 opportunities.
Paul Goldschmidt and Chris Owings also homered for Arizona, which has won five of its last seven games on the road.
Goldschmidt hit a two-run homer in the first inning off Milwaukee starter Marco Estrada. The Brewers scored for five runs in the bottom half off Josh Collmenter.
Collmenter gave up just four singles after the first.
"We did a great job offensively the first inning," Roenicke said. "Last night's game we won because we added on but we didn't do a thing after the first inning (tonight). We had (Collmenter) in pitch count trouble through three innings and then that fourth and fifth inning were really quick innings. We shouldn't have let him go that far."
Collmenter gave up five runs - one earned - and eight hits in 5 2-3 innings. He struck out three and walked one.
"I just wanted to give the team a chance to win to try and keep us in it long enough," Collmenter said.
Goldschmidt's first-inning homer came immediately after Arizona challenged a call in which leadoff hitter Gerardo Parra, who had singled, had been ruled out at first base on a pick off. The call was overturned by review.
Lyle Overbay had an RBI single, Ownings' two-out throwing error allowed another run to score, Jean Segura followed with a run-scoring single and Schafer capped the big inning with a two-run double.
Both pitchers settled down after that. Estrada retired 11 of the next 12 batters following Goldschmidt's home run before issuing a walk to A.J. Pollock leading of the fifth. Pollack later scored on Collmenter's ground out, cutting the lead to 5-3.
Owings hit his first big league homer leading off the sixth.
Estrada yielded four runs and four hits over six innings. He struck out four and walked two.
"I actually thought I threw the ball really well today," Estrada said. "I made a mistake to Goldschmidt and he hit it out. Even the other home run, I was trying to elevate on (Owings). It was a pitch I was trying to make. I made it and I got beat."