Peavy (3-5) gave the Padres' bullpen a rest, winning for the first time in six starts and running his career mark against Cincinnati to 6-0 with a 2.28 ERA. It was his first complete game of the season and seventh of his career.
Bronson Arroyo (5-3) went seven innings for the Reds and allowed all three runs.
The game Sunday zipped by in 2 hours, 14 minutes, after their 16-inning marathon lasted 5 hours, 14 minutes. They only needed three total pitchers, too, after combining for 15 in their game that ended early Sunday morning.
The last time the Padres swept a three-game at home against the Reds was June 16-18, 2000.
After Chris Dickerson led off the game with a double, Peavy retired 17 straight batters before Dickerson's solo homer with two outs in the sixth inning cut the lead to 2-1. Peavy also allowed a single to Ryan Hanigan in the eighth and a two-out single to Jerry Hairston Jr. in the ninth.
Peavy struck out eight and did not walk a batter to win for the first time since a 2-1 victory April 16 at the New York Mets. His last complete game was April 5, 2008, against the Los Angeles Dodgers.
Kouzmanoff, who singled in a run in San Diego's two-run first, hit homered off Arroyo in the eighth to knock the right-hander out of the game and give the Padres a 3-1 lead.
Kouzmanoff went 3 for 4 and is 9 for 13 in his career against Arroyo.
San Diego scored two runs in the first inning after Arroyo started the inning by walking Drew Macias and hitting Edgar Gonzalez. With two outs, Kouzmanoff singled in one run and Jody Gerut followed with a run-scoring single.
Arroyo walked the bases loaded in the fourth, but with two outs escaped the inning when Gold Glove second baseman Brandon Phillips made a diving catch of Adrian Gonzalez's line drive.
Notes:@ The Reds are the only NL team against whom Peavy has not lost. San Diego is 9-1 in Peavy's 11 career starts against Cincinnati. ... Reds 1B Joey Votto sat out Sunday after leaving Saturday night's game in the fourth inning due to mild dizziness. Votto, who is hitting .366, will be examined Monday in Cincinnati. Since May 7, he has missed five starts with the flu and left two games with dizziness.