Ottawa's Mika Zibanejad and Philadelphia's Jake Voracek each scored on the opening shots of the tiebreaker.
Neither team scored in the next three rounds. Simmonds then punched in the winner against Craig Anderson to give the Flyers their first shootout victory in six tries this season. The Flyers had lost 10 straight shootouts overall.
Mike Hoffman faked out defenceman Mark Streit in the circle and put a shot past Steve Mason to give Ottawa a 1-0 lead in the third period.
Simmonds scored his 16th goal just 1:23 later, this one from Streit and Claude Giroux on the power play.
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