McCoy finished the day completing 20-of-32 passes for 199 yards and two interceptions. At one point in the game, chants of "RGIII" could be heard from the fans at FedEx Field in Washington.
Griffin was sacked on his second play after entering the game, but finished 3-of-4 for 33 yards.
McCoy has started the last two games for Washington after Griffin was benched. Last Sunday against the Indianapolis Colts, McCoy threw for 392 yards and three touchdowns with zero interceptions in a 49-27 loss. Sunday's loss to the Rams drops Washington to 3-10 on the season.
Entering Sunday, Griffin had completed 69.7 percent of his passes for 869 yards, two touchdowns and three interceptions while going 1-4 as a starter.
Reports emerged last week that Gruden is "done" with Griffin and would prefer the team to make a "clean break" with the quarterback this offseason.
ESPN's Adam Schefter, however, has reported there is a "real chance" Griffin could be reinstated as Washington's starter at some point this season.
- Molly Geary