Despite falling short against the Brewers, the Houston Astros believe they showed that opponents can't take them for granted.

Brian Bogusevic drove in three runs, including two during a seventh-inning rally and Jed Lowrie hit his first home run, but it wasn't enough as the Astros lost 6-5 to the Milwaukee Brewers on Monday night.

Lowrie credited the team for persevering after they trailed Milwaukee 6-2 in the top of the seventh.

"We need to continue to grind it out," Lowrie said. "We're playing really competitive games right now. There's not a lot of rolling over. There's a lot of fight. Tonight, we could have easily rolled over. We made it tough on them."

Zack Greinke (2-1) had given up two runs in six innings and handed Jose Veras a four-run lead to start the seventh.

Five of the next six batters reached base as Houston scored three runs on four hits, including Bogusevic's two-run triple, before Veras struck out Jose Altuve and got pinch-hitter Matt Downs to ground out to end the inning.

Astros manager Brad Mills saw some positives coming out of the game.

"It's there," he said. "The guys are having the at-bats at those times and are at least trying to make some good, solid contact."

A bright spot was Lowrie's first home run of the season coming off Greinke in the top of the first.

"He hung a slider on the two-strike count," Lowrie said. "I was able to put a good swing on it and drive it out."

Unfortunately for Houston, Ryan Braun broke out of a 2-for-20 slump with three hits including a homer and Greinke did what he always does at Miller Park — win. Greinke struck out a season-high nine in six solid innings to improve to 13-0 at home with Milwaukee, which won its 10th straight against the Astros.

Greinke, who threw a season-high 115 pitches, said that it was a good game all around.

"It was fun," he said. "Made a bunch of good pitches. Team played a really good game."

The Astros pushed at Greinke in the fifth, but the right-hander managed to stay away from a big inning.

After consecutive singles put runners at the corners with nobody out, Greinke struck out Lowrie and J.D. Martinez. Carlos Lee singled to load the bases. Greinke walked Bogusevic to force in a run, but then fanned Chris Johnson to end the threat.

"I feel like I really struggled with guys on base," he said, even though he won his first career start at Miller Park against the Astros and kept his streak alive. "So, it was really nice to be able to get out of some jams. It definitely wasn't easy out there today."

Greinke allowed eight hits. He walked two but had those three big strikeouts in the fifth when he worked out of a jam.

With the victory, Greinke improved to 3-0 overall against the Astros. He was unbeaten in two starts at Houston last season.

Francisco Rodriguez pitched a 1-2-3 eighth and John Axford earned his 46th consecutive save — third this season — with a scoreless ninth.

Lucas Harrell (1-1) took the loss in his first start at Milwaukee and second against Greinke. Harrell allowed five runs and five hits in five innings.

He said that he got behind a lot against the Brewers.

"That's something I've been working on and it didn't really work out today," he said. "I got behind a lot and my walks really hurt me. It was just one of those days where I tried to battle."

The 26-year-old right-hander's first career start against the Brewers came Sept. 2 at Minute Maid Park. He went 5 1-3 shutout innings but eventually lost 8-2 to Milwaukee and Greinke, who allowed nine hits and two runs in six innings.

"It's frustrating for me because these guys are out there playing their asses off for me and you don't have all your stuff that day," Harrell said. "You cost your team a win. It's exciting to see the guys fight back — they really fought hard — but I didn't do my part."

Brandon Lyon took over for Harrell to start the sixth. The first five batters reached base, but the Brewers could only push across one run on a wild pitch.

It could have been worse, but Lee and catcher Jason Castro stopped the threat.

With one out and the bases loaded, Rickie Weeks fouled out to Carlos Lee, who caught the ball with his back to the plate. The first baseman turned and fired a strike to Castro, who was blocking the plate. Mat Gamel plowed into him with his left shoulder in a rough collision at the plate, but Castro hung onto the ball to end the inning.

"Carlos did a good job of turning around on the one-hop to him," Astros manager Brad Mills said. "Jason did a good job of grabbing the ball."

The Astros went ahead in the first on Lowrie's first homer of the season, but the lead didn't last long. Milwaukee moved in front in the bottom half as Braun, Aramis Ramirez and Corey Hart each drove in a run.

Gamel tacked on a run for Milwaukee with a sacrifice fly in the fourth.

Jordan Schafer doubled in the third and has reached base safely in all 17 games, the longest stretch by an Astros player at the start of a season since Craig Biggio began 2000 with a 17-game streak.

NOTES: Greinke also beat the Astros 2-1 in Houston on June 23, 2009, with Kansas City. ... Lowrie's home run was the first allowed by Greinke in 18 innings this season. ... Schafer, whose grand slam helped the Astros rout the Los Angeles Dodgers 12-0 on Sunday, had a tough first at-bat. He fouled a 90 mph fastball off his inner right calf in the first and then spent several minutes walking off the pain. He stayed in the game and doubled the next time he was up.