The Blues skated off a Dallas power play earlier in the extra time, then went on their own man-advantage when Kevin Connauton was whistled for tripping.
With time winding down, Alex Pietrangelo fed Shattenkirk in the left circle and the Blues defenseman one-timed a shot off both posts and past Kari Lehtonen for the game-winner.
Shattenkirk also got the decisive shootout goal in St. Louis' victory over Chicago Saturday.
Jaden Schwartz and T.J. Oshie scored in regulation as the Blues won for the fourth time in five games.
Brian Elliott made 28 saves.
Jamie Benn and Ryan Garbutt each scored for the Stars.
Lehtonen turned aside 19-of-22 shots.