With the Wings trailing 2-1, Datsyuk tipped in a shot by Ian White 11:19 into the final frame for the equalizer.
Kronwall notched the go-ahead goal less than a minute later with a wrist shot from the slot that got past a screened Brian Elliott, and Detroit hung on to win its 11th straight home game.
Matt D'Agostini and Alex Steen scored for the Blues and Elliott finished with 29 saves.
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