Torain ran for 135 yards, giving the Redskins a 14-0 lead with a 20-yard TD run in the second quarter, and Washington's tough defense held St. Louis to 172 total yards in the win.
They yielded 10 late points thanks to a pair of fourth-quarter interceptions hurled by Rex Grossman but held on for the win due in part to 2 1/2 quarterback sacks by Brian Orakpo.
Grossman completed 15-of-29 passes for 143 yards and a score for the Redskins (3-1).
The Rams, meanwhile, fell to 0-4 as Sam Bradford was limited to 164 yards and a touchdown on 20-of-43 passing.
Steven Jackson could manage just 45 yards on 17 carries for St. Louis.
Notable deaths of 2014 [PHOTOS]