It was the right wing's sixth goal in the new NHL season.
Miettinen was the second Wild shooter in the shootout.
He deked to the backhand to beat Mike Smith high for the lead.
In regulation, Backstrom made 32 saves, and in the shootout, he made three others for the Wild, who have begun the 2008-09 season by winning first four games.
Smith made 21 saves in regulation for the Lightning, who are winless under new Coach Barry Melrose, having lost their first five games to start the season.
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