The Buccaneers went into an early lead as rookie quarterback Jameis Winston passed to Mike Evans with his first throw of the game and the young wide receiver ran into the endzone for a 40-yard touchdown.
Cousins made up for that mistake just before the break as the QB kept the ball for himself and ran into the endzone from seven yards out for the Redskins' first touchdown of the day.
In the second half, the Redskins came out with a strong start as Cousins would pass to Ryan Grant for a three-yard touchdown to cut the deficit to 10 points.
Washington began to pick up a head of steam as Cousins would get his second passing touchdown of the day, finding returning tight end Jordan Reed for the eight-yard score to make it a three-point game as they headed into the fourth quarter.
Tampa Bay broke that 21-0 run from the home team soon afterwards as Barth hit another field goal, but the Redskins would reply with a field goal of their own in the fourth quarter as Dustin Hopkins split the uprights.
A big 49-yard run from Doug Martin brought Tampa Bay close to the endzone late in the fourth quarter but after the drive stalled, Barth had to hit another three points to give them a six-point lead with two minutes remaining.
That would not be enough as the Redskins stole the win with a two-minute drill, as Cousins found Reed again to give the home side a one-point lead with 30 seconds remaining and they forced a fumble late in the game to ensure the victory.
The Redskins move to 3-4 on the season while the Buccaneers drop to the bottom of the NFC South at 2-4.