The Cubs fell behind 2-1 in the eighth after the Cardinals' Matt Holliday socked a go-ahead, two-run homer off Carlos Marmol. Chicago's Bryan LaHair tied it up in the bottom of the ninth when he belted Marc Rzepczynski's first pitch into the left-field bleachers.
In the 10th, Tony Campana collected a one-out single off Fernando Salas (0-1), stole second, and, after LaHair was intentionally walked, came home when second baseman Tyler Green couldn't handle Soriano's sharp grounder.
James Russell (1-0) earned the win for the Cubs, who clinched their first series win of the year.
Cards starter Adam Wainwright allowed only one run on six hits over six innings.
Notable deaths of 2014 [PHOTOS]