Milwaukee led 2-1 in the ninth and handed the game to its All-Star closer, who hadn't blown a save -- or surrendered a run -- in 19 previous appearances this year. Bohm belted a leadoff homer off Hader (0-1), whose streak of 40 straight scoreless appearances dating to last season matched Houston Astros reliever Ryan Pressly for the longest such stretch in MLB history.
Two batters later, pinch hitter Vierling, in his first major league at-bat since May 10, took Hader deep again to put the Phillies in front.
It was Hader's first blown save since July 7, 2021, snapping the MLB's longest active streak at 32 consecutive converted saves, according to ESPN Stats & Information research.
"They definitely got to me today," Hader said. "Tip the cap. It definitely sucks, but it happens.''
Hader said he planned to watch video of his outing after the game and would be ready to move on by Wednesday.
"The scoreless streak, that was pretty cool,'' Hader said. "I was hoping to get another one, but it's baseball. It'll keep you honest.''
Brewers manager Craig Counsell said the team's offensive struggles didn't provide any cushion for Hader.
"Unfortunately, we could only give him a one-run lead going into that inning, and we paid a price for it,'' Counsell said. "He's been so good. It's surprising, but at some point it's going to happen.''
Connor Brogdon (1-0) pitched a scoreless eighth, and Corey Knebel closed it out with his 10th save in 13 tries. Knebel walked three batters to load the bases but struck out Pablo Reyes to end it. The Phillies are 4-0 since they fired manager Joe Girardi on Friday.
The Brewers, who on Monday had a day off for the first time since May 19, have lost four straight.
The Associated Press contributed to this report.