Aided by defensive gems from center fielder Carlos Gomez and first baseman Shane Peterson, Lohse limited the damage to four earned runs on five hits and three walks in 6 2/3 innings.
It marked the first time since July 1 and only the third time since May 15 that Lohse threw a pitch in the seventh inning, and the 18th time in 21 starts that he surrendered at least one home run.
"Except for that one inning," Lohse said, referring to a three-run Giants fourth that included Brandon Crawford's two-run home run, "I felt pretty in control. I just fell behind a couple guys, and obviously the home run hurt a lot. But I felt I had a lot better control of the game than the last couple starts."
Crawford hit his 15th home run of the season to the deepest part of AT&T Park in right-center field on a 3-0 pitch.
"He just made the couple mistakes, but obviously the one to Crawford was the costly one," Counsell said. "But he was pretty sharp outside that. ... He felt like he was in control the whole start, really. But again, the home run was the big blow."
Lohse was Milwaukee's Opening Day starter, but his season-long struggles have called into question his hold of a spot in the Brewers' rotation. Barring a trade, the Brewers currently have a six-man rotation, including three minimum-salary players pitching well (Mike Fiers, Jimmy Nelson and Taylor Jungmann) and another high salary player (Matt Garza) with two seasons after this one left on his contract.
Fiers' name has been linked to clubs like the Blue Jays in trade rumors. The Brewers would also entertain offers for Lohse and Garza, but both veterans are enduring down seasons. Lohse is earning $11 million in the final season of a three-year deal.
Adam McCalvy is a reporter for MLB.com. Follow him on Twitter @AdamMcCalvy, like him on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.