© PA Photos
The visitors dominated the first 45 minutes, asking plenty of questions of Martin O'Neill's men. They saw plenty of the ball, but were only able to create half-chances.
Itay Shechter had a penalty shout waved away by referee Chris Foy, with replays showing that any contact from John O'Shea was minimal.
The Black Cats made more of a fight of the second half, but it was still Michael Laudrup's men who looked likely to break the deadlock.
Dyer wasted the best chance of the night, shooting wide of the mark after Michu's driving run into the box helped set him up from around 12 yards out.
The Spanish striker could have won the points at the death for the Swans, but the Sunderland defence piled onto the ball in a desperate attempt to stop it from rippling the net.