The Baggies were on top in the first half and deservedly had their noses in front on the half-hour mark when the Sunderland defence failed to clear a corner. Gareth McAuley was able to direct the ball to Fletcher, who controlled it with his chest before turning and volleying past Vito Mannone.
Just six minutes later Brunt doubled their advantage with a fine strike as he made the most of a rebound after Nacer Chadli's initial effort came off the crossbar.
After a first half of just two chances, Sunderland did have some better opportunities in the second but all but one came outside of the box and the Baggies never really looked in danger of conceding.
New signing Jake Livermore was introduced for the hosts with 10 minutes left on the clock and he almost made the perfect start with a shot from 10 yards out, but the ball took a deflection off Papy Djilobodji to go wide.
West Brom are now up to 32 points and eighth in the league, four points behind Everton, while Sunderland have suffered four defeats in their last five and sit three points from safety at the foot of the table.