James Neal notched a hat-trick and added an assist to help clinch a place in the Eastern finals for the top-seeded Penguins for the first time since they last won the Stanley Cup.
Brenden Morrow opened the scoring in the seventh minute of the opening period for the Penguins who then scored three goals in the second, which proved the difference.
A power-play goal for Neal was followed by Kris Letang's blast and while Milan Michalek gave Senators' fans some hope to reduce the lead to 3-1, Evgeni Malkin quickly allayed any comeback fears to restore the three-goal margin.
Neal grabbed his second and third goals of the game in the final period.
Kyle Turris scored for Ottawa between Neal's final two goals.
Pittsburgh will meet the winner of the series between Boston and the New York Rangers. Boston lead the semi-final series 3-1, with Game Five on Saturday.