Peavy will try to lead the Giants to a three-game winning streak Saturday night against Jacob deGrom and the New York Mets.
San Francisco (59-50) is in the thick of the playoff race, so acquiring Peavy from Boston last Saturday seemed to be a good way to improve its chances.
The veteran right-hander, however, gave up four runs in six innings of a 4-3 defeat to NL West-leading Los Angeles on Sunday. He gave up three of those runs in the fifth while throwing a pair of wild pitches to match his total from his first 20 starts.
"It's going to take some time for me and (catcher) Buster (Posey) to get to know each other," Peavy told MLB's official website. "He's tremendous behind the plate. We all know how good he is. The more we're out there together, I'm sure we'll get a better feel."
Peavy yielded one run and three hits in 6 2-3 innings of a 6-3 win with the Chicago White Sox in his last visit to Citi Field on May 8, 2013. He's 6-2 with a 3.28 ERA in 11 starts against the Mets.
After scoring six runs while losing six in a row, the Giants have doubled that output over the past two games, including a 5-1 win against the Mets (52-57) on Friday.
Offense, however, may be at a premium as they face deGrom (5-5, 2.79) for the first time.
The right-hander has won four straight starts behind a 0.66 ERA, striking out 30 and walking five in 27 1-3 innings. DeGrom, who hasn't allowed a homer in his last nine outings, is trying to become the team's first rookie to win five consecutive starts since Dillon Gee from May 19-June 10, 2011.
He got closer to matching that run with another dominant performance Sunday, yielding four hits in 6 1-3 innings of a 2-0 win at Milwaukee.
"He's been very good. I guess he has to go out each time and prove it," said manager Terry Collins, who has claimed deGrom should be among the favorites for the NL Rookie of the Year award.
Collins, though, is more concerned with the Mets' bats after they were two-hit by Ryan Vogelsong in the series opener. New York has scored 11 runs while losing all four season meetings with the Giants.
Juan Lagares and Lucas Duda had the hits Friday. Lagares is 7 for 15 in the last four games after going 5 for 41 over the previous 12.
Duda homered and is batting .314 with six home runs and 13 RBIs in his last 14 games. His only hit in three at-bats against Peavy was a solo homer May 8, 2013.
Giants shortstop Brandon Crawford had three hits and drove in a run Friday. He's 17 for 34 with seven RBIs during a nine-game hitting streak against the Mets.