Jackson's big game helped provide plenty of offense for Claudio Vargas, who allowed four hits over seven innings in a 7-0 victory on Tuesday night.
Jackson, who had an RBI single earlier in the game, hit a three-run double in the seventh to open the scoring in a four-run rally that made it 6-0. His hit knocked out Peavy (1-3), who remained winless since the season opener.
"With the bases loaded and one out, I wanted to stay out of the double play," said Jackson, who hit a drive to center field. "He got something up in the zone, and I took advantage of it."
Peavy allowed five runs and 10 hits over 6 1/3 innings.
"Getting my first hit off Peavy helped," Jackson said. "I tell you, he's filthy up there. He's a great pitcher."
Jackson raised his season average to .273 after getting the previous game off. To open the road trip, he went 0-for-7 in Los Angeles.
"This is really good," Jackson said. "It gets the monkey off my back."
Vargas (2-1) bounced back from his worst outing of the season to record his first victory in three career decisions against the Padres. He struck out four and walked none in recording his first win since his opening start of the season.
"I felt pretty good out there," Vargas said. "I had my fastball and changeup. I've been working a lot in the bullpen, and that helped my confidence."
In his previous start, Vargas lasted 2 2/3 innings in a no-decision against San Francisco, giving up six runs and eight hits.
"We haven't had Claudio consistently do that," Arizona manager Bob Melvin said. "He's a tough guy. Some of the things he worked on actually paid off pretty well. A quality guy like that isn't going to be down too long."
The Padres dropped to 3-8 at home this season with only 33 runs scored. They managed only one run in dropping the two games to Arizona at the outset of a 10-game homestand.
"We've got to come out of this," Padres manager Bruce Bochy said. "It seems like we're giving (opposing pitchers) credit a lot lately. We can't get down. There is no easy answer."
Over their last eight games, the Padres have scored two or fewer runs six times.
Arizona's Craig Counsell had three hits, including a double, in his return after missing five games with tightness in his right hamstring. Luis Gonzalez added three hits, including a double, and drove in two runs.
"I just gave up a lot of hits," Peavy said. "Some on decent pitches, and some on pitches that caught too much of the plate. I just wasn't getting through the ball."
Brandon Medders pitched the eighth and Greg Aquino worked the ninth to complete a five-hitter for the Diamondbacks' second shutout of the season.
The Diamondbacks opened the scoring in the first when Orlando Hudson singled and scored on a two-out double by Gonzalez.
Counsell doubled to lead off the third, advanced on a sacrifice bunt and scored on a two-out single by Jackson to make it 2-0.
Johnny Estrada hit a sacrifice fly off Dewon Brazelton to complete the scoring in the seventh. Gonzalez added an RBI single in the eighth.
The crowd of 21,281 was the third smallest in the Padres' three seasons at Petco Park, coming one night after the all-time low of 19,718 for the series opener. ... Gonzalez's first two hits improved his career batting average against Peavy to .429 (15-for-35). ... Padres RHP Chris Young stands a good chance of making his scheduled start on Friday after having a positive response to medication for reduced blood flow to an artery in his pitching thumb, according to Bochy. ... Padres OF Dave Roberts was given the night off because of swelling in his left knee, but he was expected to be in the lineup Wednesday.