Stephane Sessegnon found the top-right corner from the left side of the penalty area to put Sunderland ahead.
Sebastian Larsson had earlier struck the Swansea post, before Scott Sinclair wasted the visitors' best chance by firing over from six yards.
Swansea dominated without threatening and Craig Gardner's late 25-yard volley wrapped up victory.
The substitute's clincher five minutes from time was a rare effort on goal from Sunderland, who hardly threatened after Sessegnon's opener.
But Swansea's inability to offer a cutting edge on their travels was again evident, with home keeper Simon Mignolet troubled only twice, consigning Brendan Rodgers's side to a seventh away defeat in 11 games.
The victory moves Sunderland above Swansea into 10th place as O'Neill collected his 10th point from a possible 12 at home since taking over.
Sunderland's opener came as a breathless opening 15 minutes ended with a moment of genuine quality.
After a quick exchange of passes with James McClean down the left flank, Sessegnon opened up his body to curl an unstoppable effort into the top right corner.
The precise strike was too good for Swansea goalkeeper Michel Vorm, who had earlier deflected Larsson's volley on to the foot of the post.
Swansea, basking in the plaudits of their 3-2 win over Arsenal last Sunday, also threatened in the opening exchanges.
Sunderland defender Wes Brown, back after a three-game injury absence, denied Nathan Dyer with a well-timed last-ditch tackle, before Phil Bardsley followed suit to stop Scott Sinclair on the opposite flank.
Sinclair was guilty of wasting a glorious chance when he blasted over from barely six yards from Dyer's low cross.
The visitors went on to dominate the rest of the half, with Gylfi Sigurdsson slotting seamlessly into the Swansea midfield as he made his first start.
His far-post cross gave Danny Graham a great chance to level, but the striker failed to keep his header down.
Despite Swansea's dominance of possession, Sunderland stopper Mignolet was not tested until the 57th minute when he palmed away Sigurdsson's free-kick.
The home crowd grew impatient as Sunderland struggled to find any cohesion, but the Black Cats suddenly came to life in the final 15 minutes.
Sessegnon headed wide from McClean's inviting cross, before Vorm needed to be alert as he rushed out to beat Connor Wickham to the ball at the edge of the box.
Wickham wasted a glorious chance to seal victory when he fired wildly wide from close range, but the points were secured when Gardner struck.
The substitute controlled Sessegnon's crossfield pass on his chest before sending a dipping 25-yard volley into the top corner.
