Beck completed 14-of-17 passes for 140 yards while the Redskins were building a 16-0 lead at the break.
Rex Grossman, who played well during Washington's victory over Pittsburgh last week, was 7-of-12 for 88 yards with an interception during the second half against the Colts.
The game's only touchdown came on a 1-yard run by Tim Hightower at the end of an 80-yard drive in the first period. Graham Gano added field goals of 28, 27 and 26 yards.
Indianapolis, playing without No. 1 quarterback Peyton Manning, got only a 55-yard field goal from Adam Vinatieri in the third period.
Washington rookie Roy Helu had 14 carries for 101 yards. Chris Painter started at quarterback for Indianapolis and was 5-of-10 for 40 yards.
The Redskins are 2-0 to start the exhibition season. Indianapolis is winless in its two games.