Soriano's first homer, a two-run shot, capped a four-run, first-inning outburst. His second, also a two-run homer, came in the fifth and gave the Cubs a 10-2 advantage.
Marlon Byrd chipped in with a two-run homer and three RBI for Chicago, which took three of four games from Arizona in the weekend series.
Gorzelanny (1-3) struck out a career-high 10 batters while allowing only two runs on six hits.
The Diamondbacks were led by Rusty Ryal, who connected for a two-run homer. Edwin Jackson (1-3) was knocked around for eight runs on 11 hits over four innings.