Tracy's homer, his fourth of the season, started the scoring in the bottom of the third, and Byrnes smacked his 11th to give Arizona a 6-0 lead an inning later.
Orlando Hudson added an RBI single; Byrnes had two runs and four hits; Miguel Montero had two runs and three hits; and Tony Clark also had two hits for the Diamondbacks -- who have won four of their last five games.
Winner Micah Owings (5-1) gave up four earned runs and eight hits in 5 2/3 innings with two walks and seven strikeouts.
Jose Valverde recorded his 23rd save.
The loser was James Shields (6-2).