Peralta allowed a one-out double to Michael Taylor in the third inning, walked one and struck out three in his second appearance of training camp. Peralta was 11-15 in 32 starts in his first full season with Milwaukee last year.
Milwaukee tagged Oakland starter Dan Straily for two runs in the second and another in the third.
Montz's home run came off right-hander Johnny Helweg, who also gave up Max Muncy's tying hit.
Brewers: Peralta struggled early last spring and vowed things would be different this year. So far, it has. In his first appearance of the spring, Peralta pitched in relief against Oakland, throwing two shutout innings.
"I prepared earlier with everything this offseason," the 24-year-old said. "I felt I had better command out there. I don't focus on velocity so much because I know it will be there. I was locating my pitches and not overthrowing."
He said he "threw a little bit of everything, a good change, a good slider when I was behind in the count. I was throwing it for strikes."
Athletics: After becoming the 11th rookie pitcher in club history to win 10 games in a season (10-8), Straily made his first start of the spring and had mixed reviews from manager Bob Melvin.
"He was putting some guys away, using his fastball and changeup. Hopefully, he will look more refined the next time out," Melvin said.
Brewers: Manager Ron Roenicke said that third baseman Aramis Ramirez, who had surgery in January to remove a non-cancerous polyp from his colon, could play in a game by this weekend.
Athletics: Melvin said that Montz, whose 2013 season at Triple-A Sacramento was cut short by shoulder surgery, will continue to DH but likely won't be behind the plate for the big club this spring.
Catcher John Jaso, reduced to DH duty last season while dealing with the effects of a concussion, was behind the plate for the first time this spring (six innings) and homered in the sixth inning to give Oakland its first run.
ON THE VERGE
The A's have been waiting for a breakout from outfielder Michael Taylor, acquired in a trade with Toronto after the 2009 season.
He has played 26 games for the A's over the last three seasons, but has spent most of his time at Sacramento. The 6-foot-5, 256 pound Taylor had two hits in 15 at-bats entering Tuesday's play, but was 3 for 3 against the Brewers.
"Maybe this will be a springboard for him, give him a little confidence. I hope he's on his way," Melvin said.
HERE WE GO AGAIN
The Cactus League season barely is a week old but the A's and Brewers will meet for the second day in a row and third time overall Wednesday at the Brewers' park in Maryvale, a Phoenix suburb. Right-handers Jarrod Parker (A's) and Yovani Gallardo (Brewers) are the scheduled starters.