Throwing just fastballs and changeups over 5 2/3 innings, Estrada allowed five hits and struck out three in 70 pitches.
"He can really pitch," Brewers manager Ron Roenicke said.
Receiving mostly cheers, Braun singled up the middle in the first inning off Josh Johnson.
Braun received more boos before his final two at-bats and hit into a fielder's choice and struck out on three pitches. That left him hitting .571 (8 of 14) as he returns from his season-ending 65-game drug suspension.
"He's squaring up a lot of balls," Roenicke said. "He's made some really nice plays in the outfield and getting used to right field.
"We don't have that much time left, so we'll probably pick up his playing time," Roenicke added.
Johnson allowed one run on two hits with a walk and three strikeouts in four innings.
Scooter Gennett had two RBI doubles for the Brewers.
Brewers: Estrada said he struggled with his fastball and changeup in his last outing, so those were his focus. He said he threw no curveballs and only one cutter.
Padres: Johnson, in good form following a miserable, injury-plagued 2013 season in Toronto, threw 39 of his 60 pitches for strikes and had an effective changeup.
"There was a lot to like today," Padres manager Bud Black said.
For a team-record fifth consecutive year, right-hander Yovani Gallardo will be on the mound for Milwaukee's opener March 31 at Atlanta.
"I'm not surprised at all," Estrada said. "If he's the guy, he's the guy, and we've got four other guys that can probably do it, also. It could have been anybody, but I'm glad it's him."
Gallardo has been sharp this spring, allowing one run on six hits in eight innings. He's struck out eight.
A cactus prevented Brewers right-hander Francisco Rodriguez from making his Cactus League season debut.
The veteran reliever was scratched as medical personnel continued to pull out spines from his left foot. Rodriguez said he stepped on the cactus barefoot in his dark backyard Monday night while bringing his son into the house.
Roenicke said Rodriguez played catch in the morning, but couldn't stay out there long. He indicated he could also miss Friday's game as the spines continue to come to the surface of the skin.
"There's always some that are going to be stuck inside," Roenicke said.
Have teammates given Rodriguez a hard time?
"A little bit, but not much," Estrado said. "It's an unfortunate situation. You don't want to kick him when he's down."
Padres: Catcher Yasmani Grandal made his first start in his second game since July ACL surgery. He played four innings and hit into a fielder's choice. . Third baseman Chase Headley (calf) ran on the field Thursday. "He's making great strides," Black said. . Right-hander Casey Kelly, recovering from elbow reconstruction surgery, is scheduled to throw his first batting practice Saturday. . Closer Huston Street (groin) is expected to pitch in a minor league game Saturday.
San Diego optioned outfielder Rymer Liriano, recovering from elbow surgery, and right-hander Keyvius Sampson to minor league camp. Non-roster invitees sent down Thursday included infielder Jonathan Galvez and right-hander Leonel Campos. Minor league games start Friday.
How serious are the basketball shooting games among Padres players? There were sounds of jackhammers Thursday morning as workers installed a permanent hoop to replace the portable one next to the batting cage.
"I didn't order it," second baseman Jedd Gyorko said, smiling, "but it's going to be nice."