The Reds, who have lost their past nine road games, were swept at both Dodger Stadium and Petco Park to go 0-6 on the West Coast trip.
The left-handed hitting Cordero hit three home runs over the first two games of the series.
He had two singles in the finale. The second, a groundball to right field, scored Matt Szczur, who had drawn a leadoff walk against Lorenzen as a pinch-hitter.
The RBI single came after Cordero mistakenly attempted to bunt, causing third-base coach Glenn Hoffman to tell him to swing away.
“We made sure that he got the message that we trusted his bat,” manager Andy Green said.
Renfroe hit Garrett’s 88 mph fastball 429 feet into the top of the second deck to score Yangervis Solarte and tie Nate Colbert for the most home runs by a Padres rookie before the All-Star break. Colbert went on to hit 24 home runs in that expansion season, 1969.
Brandon Mauer recorded his 12th save in 14 tries after Brad Hand threw a scoreless eighth.
The Reds rediscovered their home run prowess, getting solo shots from Jose Peraza and Joey Votto after not adding to the team’s majors-leading home run total in the series’ first and second games.
Peraza hit Chacin’s second pitch of the game into the left-field seats for the team’s first leadoff homer of the season. For Peraza, it was his third home run.
Votto cleared the wall in right-center field for his 19th homer.
Garrett took a 2-0 lead into the sixth before Solarte singled and Renfroe blasted the lefty’s 91st pitch of the afternoon.
The lefty starter, 25, brought in an ERA of 7.40.
“This was a great step,” Reds manager Bryan Price said. “He’s a great kid, he’s a great worker, everybody pulls for Amir to do well, and I think that was certainly a step in the right direction because he was throwing three pitches over the plate for strikes and he was on the attack.”
Zack Cozart, who went into Wednesday as the leading vote-getter at shortstop for the All-Star Game, was out of the starting lineup with a quad injury for the second day in a row. He was pulled from Monday’s lopsided game due to the quad.
Reds: RHP Tim Adelman (4-2, 4.34) on Friday will face the Los Angeles Dodgers in Cincinnati after going 2-0 with 2.08 ERA in his past four starts.