Grossman assumed the starting role for the Redskins after Donovan McNabb was traded to Minnesota following the settlement of the NFL's labor dispute.
A second-quarter 8-yard scoring pass from Grossman to Santana Moss gave the Redskins the lead in the second period but Pittsburgh tied it on a 22-yard run by Isaac Redman to end an 80-yard drive shortly before halftime.
Graham Gano produced all the second-half scoring for the Redskins on field goals of 32, 34 and 45 yards.
Byron Leftwich was 6-of-10 for 70 yards for the Steelers, defending champions of the AFC. Starting quarterback Ben Roethlisberger played only one series and was 2-of-3 for 22 yards.