Beckett pitched seven innings and had an RBI single to help Florida to the 2-0 win, the Marlins' second straight shutout over the Padres.
"You go into a game against Peavy just hoping to get a no-decision," Beckett said. "If you keep your team in the game, you feel pretty good."
Beckett (12-6) allowed four hits, two walks and struck out six in winning his fourth straight decision.
Todd Jones pitched the ninth for his 26th save. The shutout tied Florida's team record of 14 set last year.
Peavy (10-6) allowed two runs, five hits, three walks and struck out nine in losing consecutive starts for the only second time this season.
"This is as bad as it gets, I don't know what it takes to win a ballgame," Peavy said. "I'm not going to blame the hitters. I didn't do my job."
Treanor's run-scoring single in the fourth gave Florida a 2-0 lead.
Although Florida's top four hitters were a combined 0-for-13, Nos. 8 and 9 -- Treanor and Beckett -- knocked in the runs.
"We can do the same thing," Padres manager Bruce Bochy said. "We're just not doing it."
The Padres, who were shut out on five hits by Dontrelle Willis on Wednesday night, put together their most serious threat in the seventh. Beckett retired pinch-hitter Eric Young on a pop up to third with runners on second and third and one out. Then, following a walk to pinch-hitter Robert Fick, Dave Roberts struck out.
"We might be struggling but those are two good quality pitchers," Young said. "Dontrelle wasn't an All-Star for nothing. And Beckett, if he had been healthy, would have been an All-Star, too."
Florida has gone 8-1-1 in its last 10 series after beginning the season's second half by losing three of four games in Philadelphia. The Marlins are six games above .500 (63-57) for the first time since May 30.
"Another series win," Marlins manager Jack McKeon said. "We're not going to brag about it. We just want to win as many series as we can."
Peavy, the NL leader in strikeouts, has fanned nine or more in five consecutive games.
Marlins starters have a 0.95 ERA (seven earned runs, 66 innings) over the past nine games.
- The Marlins have scored first in 24 of their last 29 games.
- The Padres had been shut out 12 times this season after being held scoreless three times in 2004.
- Florida 2B Luis Castillo (strained left quad) did not start a second consecutive game. McKeon said Castillo would miss "a couple of more days, at least."