The score was tied 1-1 when Franzen lifted a wrist shot from the right circle that banked off a defenseman and Sabres goalie Ryan Miller into the net with 8:17 remaining in the third.
Jonas Gustavsson stopped 21-of-22 shots.
Cody Hodgson scored and Miller finished with 31 saves for the Sabres, who fell to 5-19-1 on the season.
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