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.
Notable deaths of 2014 [PHOTOS]