Neither side could claim they fully deserved maximum points - Sunderland failed to manage a single shot on target - but the visitors could highlight a fifth minute penalty claim after John O'Shea appeared to bring down Itay Shechter.
Danny Graham - a second-half substitute for Leon Britton and a reported Sunderland transfer target - had the chance to win it for the visitors at the death only to be denied by a goal-saving challenge by Titus Bramble.
Full-back Dwight Tiendalli whistled a shot across the face of goal but Bramble got in a priceless block to deny Graham from point-blank range.
Graham may yet become a Black Cats player in the next 48 hours but his arrival as a 75th minute substitute was greeted with boos by the home support due to his links with fierce rivals Newcastle.
Fellow substitute Roland Lamah also came close to making an impact after a sloppy pass from Seb Larsson but Simon Mignolet was off his line quickly to smother the danger.
Michu was kept quiet for large chunks of the game but he did create a great chance for Nathan Dyer only for the midfielder to put his near-post effort wide.
At the other end, Sunderland failed to test Gerhard Tremmel in the visitors' goal. The German can have had few easier nights with Black Cats' leading scorer Steven Fletcher lacking any real service.
The home side looked brighter after the interval, Stephane Sessegnon probing the Swansea defence, but it was a comfortable evening for Ashley Williams and company who stifled what little threat Sunderland mustered with relative ease.