Datsyuk got control of the puck in the left circle as the clock ticked down. After making a move on an Anaheim defender, he fired a wrist shot past Curtis McElhinney and into the net for the Red Wings' third straight win.
Detroit netminder Jimmy Howard made 21 saves.
The Ducks got a goal and an assist from Bobby Ryan while Ryan Carter, Danny Syvret and Teemu Selanne also found the net.
Anaheim received 36 saves from McElhinney in the loss.
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