Dellucci, who went three for three and also scored twice, hit his grand slam in the second inning off Todd Ritchie.
Quentin McCracken and rookie Lyle Overbay added three hits apiece for the Diamondbacks, who built a 9-1 lead after three innings.
John Patterson, who already has secured a spot in the Arizona rotation, gave up one run and eight hits in five innings. The righthander struck out two without a walk.
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