Staal got control of the puck during a scramble in front of the Senators' goal and fired into an empty net to give the Penguins a 2-0 lead 1:21 into the period.
Ben Lovejoy and Matt Cooke scored within the next 6 minutes and the Penguins cruised to their fourth win in five games.
Staal and Tyler Kennedy each finished with a goal and an assist, Chris Kunitz added three helpers and Brent Johnson made 21 saves for Pittsburgh.
Ryan Shannon got the only goal for the Senators, while Craig Anderson yielded five scores on 41 shots.
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