Sunderland enjoyed the better of the chances in a goalless first half as Lukasz Fabianski needed to be alert to deny Adam Johnson and Santiago Vergini with smart saves, while Swansea were mainly limited to efforts from range.
Swansea did test Vito Mannone after the break through Gylfi Sigurdsson’s strike, but Connor Wickham passed up the best opportunity for the hosts as he headed Sebastian Larsson’s cross over the bar from inside the area.
The Swans had full-back Angel Rangel dismissed with 10 minutes remaining after he was shown a second yellow card for blocking Will Buckley, while substitute Steven Fletcher nodded a glaring chance wide in the closing stages for the hosts.
Sunderland head coach Gus Poyet had expressed his admiration for the Welsh side’s approach and predicted a difficult afternoon for his players.
But his tactical plan, designed to frustrate the visitors, worked well in the opening 45 minutes and Garry Monk’s men could not muster a single attempt on target despite enjoying sustained periods of possession.
Indeed, it was the Black Cats who created all the better chances in the first half, forcing Fabianski to earn his money with a series of important saves.
Johnson was first to call upon the Poland international when he met Wickham’s 12th-minute flick-on beyond the far post and drilled in a half-volley from a tight angle which Fabianski did well to turn away.
The keeper had to sprint from his line four minutes later to prevent Buckley from latching on to Larsson’s through-ball with Sunderland finding their stride.
Swansea were prospering out wide with Nathan Dyer and Wayne Routledge seeing plenty of the ball as Jonjo Shelvey and Sigurdsson kept the supply lines open.
But they were able to create little of note with Dyer twice failing to come anywhere near hitting the target after working himself into promising positions.
By contrast, Sigurdsson had to get in an important 35th-minute block to repel Lee Cattermole’s well-struck volley, and Fabianski was very nearly caught out by Vergini’s looping header seconds later, eventually throwing out a hand to turn it away at the last minute.
Swans striker Bafetimbi Gomis fired tamely high and wide five minutes before the break after turning marker John O’Shea, but Sunderland keeper Mannone headed for the dressing room having not had a save to make.
Ki Sung-yueng blazed high over the bar four minutes after the restart with the Welsh side increasing their tempo, and there was an anxious moment for Vergini seconds later when he stuck out a leg as Routledge went past him into the box and went to ground, although referee Chris Foy was unmoved.
Mannone was called upon for the first time with 57 minutes gone to keep out Sigurdsson’s dipping effort from distance, but did so with little discomfort.
The game became increasingly physical as it wore on with Ashley Williams and Wickham in particular becoming embroiled in a wrestling match.
Poyet looked to inject fresh impetus by replacing Johnson with Ricky Alvarez with 24 minutes remaining, and the Argentinian had an immediate impact as he targeted full-back Neil Taylor and covering midfielder Routledge.
It was the Black Cats’ turn to look in vain to Mr Foy after Wickham appeared to be dragged to the ground inside the box by central defender Federico Fernandez with 68 minutes gone with time fast running out.
They came agonisingly close to snatching the lead three minutes later when Buckley slipped past Fernandez and drove the ball across goal, where Taylor did just enough to prevent Wickham making contact in front of a gaping goal.
But the former Ipswich striker was guilty of a glaring 74th-minute miss when he met Larsson’s cross unopposed, but powered his header harmlessly over the bar.
With Rangel having departed after bring down Buckley to earn his second yellow card, Fabianski plucked Larsson’s 83rd-minute free-kick from under his crossbar and Fletcher headed a cross from the impressive Alvarez just wide seconds later as the visitors stood firm.