Peavy, who turns 24 on Tuesday, has emerged as the Padres ace with a 5-0 record and 2.00 ERA in 10 starts.
The young right-hander pitched a two-hitter for his first career shutout in a 10-0 victory over the Arizona Diamondbacks in his last start on Thursday.
San Diego had used 13 pitchers in its previous two games before Peavy’s gem.
“Jake is mature well beyond his years,” Padres outfielder Dave Roberts said. “To see that our bullpen went through some things the last couple of nights, for him to take the mound to be the stopper and to go so deep in the game, he stepped up.”
The 24-year-old ace walked none and needed only 94 pitches (65 strikes). He had seven strikeouts or more in eight of his nine previous starts, but struck out just two Thursday as he conserved energy so he could finish the game.
“It’s very satisfying,” said Peavy, who lowered his ERA to 2.00 after leading the NL at 2.27 ERA last year.
Peavy will try to close out a successful month for the Padres, who have a 21-6 mark in May.
Pinch-hitter Miguel Ojeda doubled in the winning run with two outs in the ninth inning and San Diego beat Milwaukee 2-1 on Monday.
The Padres extended their lead in the NL West to a season-high three games over idle Arizona. San Diego won its fifth straight game overall and tied the franchise record with its 10th straight win at home.
The Brewers were held to six hits as they dropped the first game of a seven-game road trip. Milwaukee has lost three in a row to fall nine games behind St. Louis in the NL Central.