Estrada pitched five innings in a spot start, combining with four relievers on a three-hitter, and Yuniesky Betancourt homered to carry the NL Central-leading Brewers to a 1-0 victory over the Pittsburgh Pirates on Saturday.
"I was trying to give the guys at least six, seven innings," Estrada said. "Fortunately, it was only five, but you know (it) kept us in the game. That's all that matters."
Pirates manager Clint Hurdle tipped his cap to Axford, but really thought his team should have been able to plate a run.
"He's got a quality fastball, big-time breaking ball," Hurdle said of the Brewers' closer. "Unfortunately, we weren't able to produce when we had the opportunity. We needed to find a way to score that run and we didn't do it. You give their closer some credit, but that's an opportunity that we need to cash in."
Estrada said the bullpen sealed the victory.
"The bullpen came in and did an outstanding job," he said. "We got a win. That's what matters."
Estrada (3-8) took the mound for Chris Narveson, who was placed on the disabled list Wednesday with a cut thumb on his throwing hand.
Kevin Correia (12-11), who leads the majors with 10 wins on the road this season for Pittsburgh, lost for the second time this season at Miller Park.
Estrada retired the first seven batters before Ronny Cedeno lined a single to left with one out in the third. He advanced on Correia's sacrifice, but second was as far as any Pirate got in five innings as Estrada caught McCutchen looking to end the inning.
Estrada said that "first inning had a lot of adrenaline going" since it had been a while since his last start.
"I told myself to, 'Relax, calm down. You've done this before. Go out there and throw strikes,", he said. "And, that's pretty much what happened."
He retired the side in order in the fourth and fifth before being lifted for Zack Greinke, who pinch hit for him in the bottom of the fifth. Greinke wore Sunday's special jersey with Bierbrauer across the front of the jersey. No protest was raised after he bunted to advance Lucroy to second.
Brewers manager Ron Roenicke said that Greinke didn't know he had the wrong jersey on. Roenicke predicted he'll get a memo from MLB about not letting that violation happen again. He added that if it did, a fine would be the next step.
Still, he wasn't displeased with Greinke.
"If he bunts like that, he can wear whatever he wants," Roenicke said in jest.
Estrada struck out five in his fifth start and 33rd appearance of the season. His other win came April 6, the same day his contract was selected from Triple-A Nashville. He beat Atlanta at home in a start for Greinke, who was on the disabled list with a cracked left rib.
Narveson needed eight stitches to close a deep slice across the top of the thumb on his throwing hand. He cut it Tuesday while using scissors to repair his glove.
Betancourt fouled off the first two pitches from Correia before sending the third to the bleachers in left for his ninth home run of the season.
The Pirates had been providing more than six runs in support of Correia, but came up empty against Estrada and company.
Correia, who came in leading the majors with 10 road wins this season, worked 6 2/3 innings and allowed seven hits.
Milwaukee (69-51) improved to a major league-best 43-15 at home with the 11th win in their last 12 games at Miller Park.
It was Milwaukee's 11th straight win and 33rd in 35 games when Pittsburgh visits, dating to May 4, 2007.
The Pirates placed 1B Derrek Lee on the 15-day disabled list before the game. He broke a bone in his left wrist when he was hit by Chicago's Carlos Marmol on Aug. 3. The move is retroactive to Aug. 10. Lee, who was acquired from Baltimore on July 30, missed four games, but returned Monday and played two games in San Francisco. He was batting .278 with two home runs and three RBIs in five games since the trade. ... INF Josh Harrison was recalled from Triple-A Indianapolis. He went 25-for-95 (.263) with five RBIs and 12 runs scored in 30 games in two previous stints this season. ... Brewers reliever Rodriguez left Friday night's game with a leg cramp after getting his first career hit in the eighth inning against the Pirates. ... RHP Charlie Morton (9-6, 3.56) starts Sunday for the Pirates. He has gone 6-2 with a 3.29 ERA in his 10 starts on the road this season, including wins in fours of his last five decisions. ... RHP Shaun Marcum (10-3, 3.62) makes his 25th start of the season Sunday and second career against the Pirates who he beat 6-0 on April 13 at PNC Park. He has made 14 quality starts this season during which the team is 12-12.