Pittsburgh is winless in its last 16 home games.
Three of the four first-period goals came on the power play as the Predators finished the contest a team-record six for 10 with the man advantage.
Zidlicky's goal, a wrist shot past rookie goaltender Andy Chiodo after a crisp pass from Steve Sullivan on the left wing, came 22 seconds after Penguins defenseman Brooks Orpik was handed a penalty for slashing.
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