The Scotland international, back in the side after missing the Chelsea defeat with an ankle problem, grabbed his seventh of the season with an audacious flick in the 28th minute after James McClean had drilled the home side into an early lead.
Stephane Sessegnon made the game safe in added time to secure a welcome triumph for manager Martin O'Neill on the one-year anniversary of his first game in charge as the Black Cats climbed out of the Premier League drop zone on a chilly evening on Wearside.
But the defeat was a fifth in succession for the Royals, with Brian McDermott's men remaining six points away from a position of safety to increase the pressure on their boss on his debut season in the Premier League.
There was an explosive start to the contest as McClean fired home from the edge of the box with only three minutes on the clock after Adam Federici's weak punch following Adam Johnson's corner.
Nicky Shorey shot over top as the Royals sought an instant response, while Alex Pearce clipped a free-kick from the full-back narrowly wide of the post with Simon Mignolet rooted to his line.
But the Black Cats could have been further ahead as Sebastian Larsson burst through after a neat one-two with Fletcher and drew a fine save from Federici following his powerful drive from just outside the area, and then Johnson rippled the side-netting with another low effort.
Sessegnon was the next to threaten for the Wearsiders, taking Jack Colback's pass in his stride before executing a superb turn away from the defender to create space only to lash his shot wide of Federici's goal.
But it was 2-0 just before the half-hour mark after a touch of class from Fletcher as the £12million summer signing received Danny Rose's low cross with his back to goal and beautifully back-heeled it beyond Federici.
Both Rose and Johnson required treatment before the interval after ankle and leg injuries, respectively, with the winger unable to continue after half-time and the on-loan Tottenham full-back departing to chants of 'sign him up' in the 69th minute.
Mignolet was under-employed for huge chunks of the contest but had to be alert to palm away a dangerous free-kick from Shorey from the corner of the area, while the Black Cats suffered yet another injury blow when half-time substitute Bardsley limped off with 15 minutes to go.
McClean had a glorious chance to make it 3-0 after being released by Sessegnon only to see Federici make a fine save, while Noel Hunt's header from Shorey's corner in the closing stages was again repelled by Mignolet, before Sessegnon burst clear in injury time to round the keeper and roll home.