Nathan Dyer, Marvin Emnes and Wilfried Bony got the goals for the Swans in their first game since appointing Garry Monk as their manager on a permanent basis, with Fabio Borini offering the only response from the hosts.
It took just seven minutes for the visitors to break the deadlock on Wearside, with Wayne Routledge threading a perfectly-weighted pass in behind Phil Bardsley for Dyer to collect and curl left-footed into the top corner from a tight angle.
Swansea were then two-up inside the opening quarter-of-an-hour as Emnes span past John O'Shea on the edge of the box and rifled into the roof of the net, giving Vito Mannone no chance.
Sunderland - who went into the game on the back of a four-match winning run which had preserved their Premier League status - came within the width of a post of finding a route back into the game before the interval, but a speculative cross-shot from Sebastian Larsson cannoned back off the woodwork.
A reply was offered within five minutes of the re-start, as Borini's powerful header from a corner beat Gerhard Tremmel, but Swansea's two-goal lead was restored inside four minutes as Emnes cut back for Bony to drill in off the base of the post.
Whether it was the mental and physical effects of a tense few weeks or simply a bad day at the office, Sunderland were torn apart inside the opening 15 minutes of their latest outing and found themselves facing the steepest of climbs.
Monk, taking charge for the first time since his appointment was confirmed, made six changes and two of those who benefited from his largesse took full advantage.
Dyer could hardly believe his luck when, with just seven minutes on the clock, Routledge played him in behind left-back Bardsley, but he kept his nerve to lift a deft shot over the advancing Mannone and into the back of the net.
Not to be outdone, Emnes demonstrated his prowess seven minutes later when, after receiving strike partner Bony's pass with his back to goal, effortlessly turned O'Shea and blasted a left-foot shot past the Italian keeper.
Sunderland, who were struggling to contain Routledge and Dyer in particular, finally started to find their feet and worked their way into the game, but were rarely able to find a final ball to trouble Tremmel in the Swansea goal.
Indeed, the German's most anxious moment came when Larsson's 27th-minute cross flicked off defender Jordi Amat's head and came back off the foot of the post.
The Black Cats started the second half with much greater urgency than they had the first, and they were back in the game within five minutes when Borini met Adam Johnson's corner at the near post and headed firmly past Tremmel.
The Swansea keeper preserved his side's lead with a solid diving save after Johnson had cut inside and unleashed a left-foot shot seconds later and the mood inside the Stadium of Light had altered dramatically.
However, the visitors responded in determined fashion and re-established their advantage with 54 minutes gone when Jack Colback could only help Emnes' cross out to Bony, who stepped outside Bardsley before firing home off the inside of the post.
Tremmel had to get down well to keep out Larsson's swerving 71st-minute free-kick and substitute Ondrej Celustka could not convert the rebound from a tight angle.
The game ambled towards its conclusion with both sides still committing men in attack, but safe in the knowledge that there was little at stake other than pride.
Substitute Jozy Altidore might have ended a difficult season in style with an 84th-minute missile which flew just high and wide, but that was as good as it got.