On the goal, Alex Steen skated down the left side with the puck as time was running out in the period and found Shattenkirk alone in the slot.
The St. Louis defenseman guided a wrist shot past Mathieu Garon for a 2-0 lead, topping off a period in which the Blues outshot the Lightning 11-2.
Kurt Russell and T.J. Oshie also scored.
Brian Elliott notched a 19-shot shutout, his second whitewash of the year, to help secure the Blues their fifth win in six home games.
Garon finished with 24 saves for the Bolts, who saw their three-game winning streak snapped.
Celebrity Families of 2014 [PHOTOS]