With the tiebreaker knotted at 3-3, Shattenkirk beat Corey Crawford with a high shot on the goalie's left side.
Chris Stewart, Andy McDonald and Alexander Steen also connected in the shootout as the Blues bounced back from a 2-1 deficit after two periods and ended a seven game (0-3-4) losing streak in Chicago.
St. Louis' Adam Cracknell scored his first two goals of the season and David Backes added a goal early in the third period.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads