Reynolds sent a clean, opposite-field single to right field on Peavy's 107th pitch Saturday night. It was the only hit off Peavy, who was lifted after 7 2-3 innings with the Giants ahead 3-0.
It was the second time in five days that a San Francisco pitcher carried a no-hitter into the eighth inning. Madison Bumgarner's bid for a perfect game against Colorado ended with Justin Morneau's leadoff double in the eighth Tuesday night.
Peavy, acquired from Boston last month, struck out eight and walked three. He was pulled after throwing 113 pitches.
Scooter Gennett made a bid for Milwaukee's first hit in the seventh, but shortstop Brandon Crawford made a diving stop up the middle to start an inning-ending double play.
Crawford also robbed Aramis Ramirez of a hit in the fifth, going deep into the hole to grab a grounder before making a jump throw to first.
Peavy, the 2007 NL Cy Young Award winner with San Diego, has never pitched a no-hitter. He got his 2,000th career strikeout when he fanned Ramirez leading off the second.
Peavy took a no-hitter into the seventh inning Aug. 2 at the New York Mets.