ST. LOUIS -- The Brewers got just what they needed on Sunday.
Zack Greinke allowed one run over six innings and a three-run sixth inning and a solid performance from the bullpen allowed the Brewers to head to San Diego with a 3-2 victory over the Cardinals in front of a sellout crowd at Busch Stadium.
"We definitely wanted to come away with a win here," closer John Axford said. "Doing it today and the way that we did today with a great pitched game, some clutch hitting and clutch defense, too, coming up when we needed to, I think that's a great note to leave on."
Axford converted his 48th straight regular-season save opportunity, which is the fourth-longest streak in Major League history, and Milwaukee has won 51 consecutive games in which it has led after the seventh inning.
"When we are up and going into the seventh, eighth and ninth inning, we feel really good with our bullpen," manager Ron Roenicke said. "I know they scratched out a run there off Frankie [Francisco Rodriguez] and certainly got 'Ax' in trouble, but when we get a lead late in the game we feel great."
The Brewers (10-12) had lost three straight games, six consecutive road games and their first three games on Sundays this season.
"They have a pretty good team here, a pretty tough club," catcher Jonathan Lucroy said. "They are playing pretty well lately. I think it says a lot about us, getting it put on us the first few games of the series and coming out today and fighting and scratching out a win against a pretty tough ballclub."
The Cardinals (14-8) scored first with Rafael Furcal's two-out opposite-field RBI single past third base in the second inning. They missed an opportunity to add another run in the fifth when pitcher Jaime Garcia didn't tag up from third on a fly ball to center field for the second out.
St. Louis was 2-for-14 with runners in scoring position, with 13 runners left on base.
"That's the game," Cardinals manager Mike Matheny said. "We had opportunities. That's all you can ask for. We just have to get the timely hits and the situational hitting."
Carlos Gomez led off the Brewers' three-run sixth with a single to left off Garcia and scored on a single by Aramis Ramirez. Corey Hart followed with a single and then Ramirez and Hart both scored on a line-drive two-run double off the left-field wall by Lucroy to make it 3-1.
"I was looking for a ball up in the zone I could really drive and left there for me," Lucroy said. "I tried to hit the ball hard, and it ended up working out."
The three-run sixth allowed Greinke (3-1), who admitted that he wasn't sharp, to leave the game in line for a victory. He allowed one run on seven hits, struck out two and walked four in six innings.
"It was a battle for him," Roenicke said. "First five innings the leadoff batter was on base. That's not really the way Zack pitches, but I thought he battled great. I thought he threw some really good fastballs at times that were down in the zone. ... He threw some nice changeups. His cutter was good again. But it was a battle for him."
Reliever Jose Veras ran into some trouble in the seventh with a leadoff walk to Jon Jay and then a single by David Freese, but Kameron Loe put out the fire by retiring Yadier Molina on a groundout.
Rodriguez allowed a run in the eighth. Matt Carpenter led off with a double, went to third on a single by Skip Schumaker and scored on an RBI fielder's choice by pinch-hitter Daniel Descalso to make it 3-2.
Axford escaped a first-and-third, no-out jam by striking out Freese and Molina and watching pinch-runner Tyler Greene get caught stealing at the plate in a game-ending rundown.
With that, Axford moved past Brad Lidge for the fourth-longest consecutive saves streak in the history of the stat.
The top three streaks belong to Eric Gagne (84), Tom Gordon (54) and Jose Valverde (51).
"I guess it was best-case scenario after first and third with nobody out," Axford said. "I was really hoping to get Freese on a strikeout after that. If I can get a ground ball that's hard enough hit to get a double play -- just keep it out of the outfield at any cost. Luckily it just kind of worked out with a strikeout and an I-don't-know-what play."
Nate Latsch is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.