After throwing three interceptions in Dallas' season-opening 24-17 defeat to Jacksonville, Bledsoe completed 19-of-38 passes for 237 yards.
The Cowboys' offensive line allowed him time to throw and also opened running lanes for Julius Jones and Marion Barber, who combined for 133 yards on 28 carries.
However, all the news was not good for Dallas, which learned after the game that star wide receiver Terrell Owens suffered a broken finger on his right hand and is expected to miss two to four weeks.
"I feel like I'm a quick healer," Owens said afterwards. "It starts tomorrow. Once we have the surgery, we'll just try to get back. It came at a pretty good time. Obviously, we have a bye week, so I have at least two weeks to heal."
Jones rushed 20 times for 94 yards and Barber had a one-yard touchdown plunge for Dallas (1-1), which snapped a two-game skid to Washington (0-2) and avoided consecutive home losses to the Redskins for the first time since 1987-89.
Terry Glenn led Dallas with six catches for 94 yards and a touchdown, but Owens was held to three catches for 19 yards - all in the first quarter.
Brunell finished 18-of-33 for 197 yards with one interception and was sacked six times.
The southpaw threw for 128 yards on the Redskins' final two possessions when the outcome basically was decided.
Ladell Betts had 11 rushes for 40 yards and seven catches for 57 yards, but Washington's offense still appeared lost at times without star running back Clinton Portis, who sat out with a shoulder injury after playing through the pain in Week One.
The Redskins were outgained, 367-245, and committed 11 penalties for 117 yards.
They converted just 2-of-14 third downs and managed only one sack against Bledsoe.
The Cowboys initially took a 10-0 lead in the first quarter as Mike Vanderjagt kicked a 26-yard field goal and Bledsoe hooked up with Patrick Crayton for a four-yard TD pass on consecutive possessions.
Dallas pushed its advantage to 17-3 with 8:38 remaining in the second quarter as a 41-yard interference penalty on cornerback Kenny Wright set up Barber's TD plunge on 4th-and-goal.
The Redskins finally received a spark on the ensuing kickoff as Rock Cartwright split a pair of Cowboys at midfield en route to a 100-yard touchdown return.
But that really was the lone bright spot for Washington, which had as many penalties (six) as first downs in the first half and did not fare much better thereafter.
Midway through the third quarter, Redskins safety Sean Taylor stripped Barber at the Cowboys 42.
But four plays later, Brunell lofted an ill-advised pass down the left sideline that was intercepted by Pro Bowl safety Roy Williams at the 1.
Even still, Washington had a chance to pin Dallas deep its own territory.
But an immediate interference penalty on cornerback Carlos Rogers gave the Cowboys breathing room, and Wright committed a 15-yard facemask penalty, setting up Bledsoe's 40-yard touchdown bomb to Glenn.
Vanderjagt, who sat out last week with a groin injury, kicked a 50-yard field goal with 7:43 remaining to cap the scoring.
Despite the win, Cowboys coach Bill Parcells said afterwards, "I just want my team to play better. It is hard on me, it really is. I am feeling ill right now. Literally. I just want us to play better."
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