The Penguins swept the home-and-home series, winning 4-3 in overtime at PPG Paints Arena on Thursday.
Bryan Rust had a goal and an assist, and Yegor Chinakhov scored for Pittsburgh (19-12-9). Parker Wotherspoon had two assists, and Stuart Skinner made 11 saves.
"Any time you get 12 shots against a very good team like that, it is very impressive by the defense," Skinner said. "We didn't give them anything all night."
Alex DeBrincat scored for Detroit (24-15-4), which had a season-low 12 shots on goal. John Gibson made 27 saves.
"It's evident that we have work to do," Red Wings coach Todd McLellan said. "The Pittsburgh team was everything we wanted to be tonight -- they started with intensity that backed us off, they were faster than we were, and they smothered us in all three zones."
Rust gave the Penguins a 1-0 lead at 3:44 of the first period, taking a cross-ice pass from Crosby and beating Gibson from the left face-off circle.