The Penguins won their second straight with Fleury picking up his second shutout of the season and the 25th of his 10-year career.
Pittsburgh peppered Braden Holtby with 40 shots and he could not withstand the assault as Washington had a three-game winning streak snapped.
Pittsburgh extended its lead over Washington in the Metropolitan Division to three points.
Millions of Getty images now available for free via embed tool
Ray Liotta sues skin care company over use of likeness