Soriano's blast over the left-field bleachers with Bryan LaHair aboard erased a 7-6 deficit and boosted the Cubs to their first victory since May 14, snapping their worst skid since 1997.
Randy Wells (1-1) earned the victory after holding the Rockies to one run over 1 1/3 innings in relief of starter Travis Wood.
Alex Hinshaw (0-1) was tagged with the loss for San Diego after surrendering Soriano's blast.
Chase Headley went 4-for-5 with pair of homers and three RBI for the Padres, who fell for the seventh time in eight games.
Will Venable and Everth Cabrera added solo shots in the setback.