Alfonso Soriano and Kosuke Fukudome each had two doubles and three hits, Bobby Scales added his first major league home run and Harden won his fourth straight decision for the Cubs.
Peavy (2-5), whom the Cubs were interested in obtaining in the offseason, is the last Padres starter to get a win, on April 16. San Diego has lost nine straight road games, and four in a row overall.
Off to a poor start after signing a three-year, $30 million deal, Bradley admired his 439-foot homer to deep center, his fourth of the season, before rounding the bases. He has a five-game hitting streak, but came into Tuesday's game hitting .179 with only six RBIs.
Scales' home run came as a pinch-hitter in the seventh, and the 31-year-old career minor leaguer has hit safely in the first five games of his major league career.
Backed by an early lead, Peavy got out of several jams before Soriano's RBI double in the fifth made it 2-1.
Fukudome led off the sixth with a double and after Derrek Lee struck out, Bradley drove a 1-0 fastball from Peavy to right-center to give the Cubs their first lead.
Peavy gave up three runs on six hits in six innings, striking out nine and walking two.
Harden (4-1) retired 13 in a row after Adrian Gonzalez's two-run homer in the first. He gave up two runs on four hits in six innings. He struck out five and walked one. Aaron Heilman, Carlos Marmol and Kevin Gregg pitched three scoreless innings.
Brian Giles led off the game with a double and one out later, Gonzalez hit his 11th homer of the season.
Soriano added an RBI single in the eighth, and Micah Hoffpauir scored on Cla Meredith's wild pitch.
Notes:@ Padres 2B David Eckstein was in the lineup after getting hit in the ribs by Houston's Roy Oswalt on Sunday. Eckstein was a gametime decision. ... The Padres are 6-17 since Peavy's last win. ... Lee returned to the lineup after missing five games with a bulging disc in his neck. He struck out three times, with a walk. ... Cubs injured RHP Carlos Zambrano will test his strained left hamstring in a rehab start this weekend in Clearwater, Fla. He could return to the rotation on May 22 in San Diego. ... Padres RHP Cha Seung Baek's rehab will go on indefinitely after he injured his elbow pitching in the minors Saturday. Baek's MRI came back negative but San Diego manager Bud Black said Baek won't be throwing anytime soon.