Parker, who had been out since suffering a sprained right knee Sept. 21 at Philadelphia, had 70 yards on 21 carries with a touchdown as the Steelers improved to 6-2 at the midway point of the season.
Washington falls to 6-3.
But the injuries to Roethlisberger and Miller could keep them out of the Steelers' game next Sunday at Heinz Field against Indianapolis.
Roethlisberger, who was 5 of 17 for 50 yards and an interception, re-injured his sprained right shoulder suffered in the season-opener against Houston, while Miller suffered a sprained right ankle.
Despite a terrible first half offensively, the Steelers took a 10-6 lead into the half thanks to a 35-yard Jeff Reed field goal and a one-yard touchdown plunge by Roethlisberger.
A 43-yard pass interference penalty on Washington cornerback Carolina Rodgers was the big play on the drive for Reed's field goal, while Roethlisberger's TD run was set up by a blocked punt by linebacker Andre Frazier.
Cornerback William Gay recovered the ball at the Washington 13 and Roethlisberger got into the end zone on a sneak with 32 seconds left in the first half to give the Steelers their first lead.
Washington scored its first six points on a pair of Shaun Suisham field goals on two drives that totalled 14 yards.
The Steelers attempted a surprise onside kick to open the game, with Washington recovering at the 41. Gay was offsides on the kick, giving the Redskins the ball at the Pittsburgh 36 to open the game.
That set up a 44-yard Suisham field goal.
Byron Leftwich relieved Roethlisberger in the second half and connected on his first pass, a 50-yarder to Nate Washington that set up a one-yard TD plunge by Parker. Reed, however, missed the PAT and Pittsburgh settled for a 16-6 lead.
Leftwich, who completed 7 of 11 passes for 129 yards, then finished off the Redskins by tossing a 5-yard TD pass to Santonio Holmes for a 23-6 lead with 11:58 remaining.
The Steelers limited Clinton Portis, who entered the game with an NFL-high 944 yards rushing, to 51 yards on 13 carries and also recorded seven sacks.