Henrik Zetterberg assisted on Smith's score early in the middle frame and helped out on a third-period tally by Valtteri Filppula for the Red Wings.
Damien Brunner and Johan Franzen scored for seventh-seeded Detroit, which returns home to host Games 3 and 4 in the forged a 1-1 tie in the Western Conference semifinals.
Jimmy Howard turned aside 19-of-20 shots in the victory.
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