Recalled from Triple-A, Bradley (2-0) allowed three runs, four hits and a walk. His innings total was his big league high.
Paul Goldschmidt had two hits and two RBI. He is hitting .348 (14 for 46) in his last 13 games.
Drew Pomeranz (4-5) gave up a season-high six runs, five hits and four walks in five innings with nine strikeouts. His ERA, which had been second to the Dodgers' Clayton Kershaw among qualifying pitchers, rose from 1.70 to 2.48.
Brad Ziegler pitched a hitless ninth for his ninth save in nine chances. San Diego has lost six of seven and 10 of 13.
Brandon Drury, batting cleanup for the first time in his big league career, hit into an RBI forceout in the first, the first run Pomeranz allowed in a first inning this season.
Christian Bethancourt hit a tying single in the second but Chris Owings' solo homer in the bottom half put Arizona ahead for good. Bradley's bunt single drove in Chris Herrmann and Nick Ahmed beat Alexi Amarista's throw home on Gosselin's bouncer to second. Padres manager Andy Green challenged the call, which was upheld in a video review, and Goldscmidt hit a two-run double for a 6-1 lead.
Alexei Ramirez hit his first home run for the Padres in the fifth.
Padres: San Diego placed Saturday night's starter, Cesar Vargas, on the 15-day disabled list with right elbow soreness. RHP Leonel Campos was recalled from Triple-A El Paso for his third stint in the majors this season, and he pitched in relief Sunday.
Padres: Andrew Cashner (2-4) will make his second start since coming off the 15-day disabled list when he starts Monday at Seattle.
Diamondbacks: Edwin Escobar will make his Diamondbacks debut Monday against Houston in Phoenix. Escobar was claimed April 29 from Boston and has been pitching at Triple-A Reno.