The Black Cats took an early lead after Liam Hunt headed home a Tom Procter corner.
Samuel Lusale came close to an equaliser later in the first half, when he effort was deflected on to the post.
Darren Fletcher's side created a few good chances on the other side of the interval, but were unable to breach the visitors' goal on a blustery Saturday afternoon.
FIRST HALF
The visitors raced out of the blocks on the referee's whistle, and got their reward in the fourth minute when Hunt nodded in Procter's corner, although there appeared to be some deliberation between the pair about whether the touch came before the ball crossed the line.