It left Francisco Rodriguez, who has a 0.00 ERA through his first 16 appearances, as the only Brewers reliever yet to surrender a run.
"I never thought I would get through the season without giving up a run," Smith said with a shrug. "My job when that happens is to get people out and try not to give up [more] runs."
Smith did that by striking out Matt Adams and Yadier Molina, stranding the go-ahead runner at third base.
Entering Wednesday, Brewers relievers had a 2.16 ERA, trailing only the Padres (1.81) and Giants (2.06) in the Major Leagues. Opponents entered the day hitting .194 against Milwaukee's relievers.
"I don't think it's surprised us; we believe in ourselves and we believe in each other so much," Smith said. "We feel like we can shut down anything, any time we go out there. It's a lot of fun."
Smith has mostly been a starting pitcher in his career, and he said the heavy workload so far has not presented any problems.
"This is kind of a break for my arm," Smith said. "I don't mind it. Hopefully, it's only 10-15 pitches every outing. I still feel fine every day."
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.