It's Beck's first regular-season action since 2007, when he was with the Miami Dolphins.
Beck came on to begin the fourth quarter Sunday after Washington's previous drive ended with Grossman's fourth interception of the game.
After that turnover, fans started chanting, "We want Beck!" as the backup QB warmed up on the sideline.
Grossman was 9 for 22 for 143 yards and the four turnovers.