A goal from Javier Hernandez at the Liberty Stadium was enough to keep Manchester United hanging on to the coat-tails of Premier League leaders Manchester City.
The 23-year-old Mexican striker struck after 11 minutes to leave United five points behind their city rivals.
Swansea gave it a go in the second half and perhaps deserved a point if only for the manner in which they approached their biggest game in years.
Still, last season's Championship play-off winners saw their unbeaten home record go despite golden opportunities for Scott Sinclair, Mark Gower and Neil Taylor.
Desperate to close the gap on the runaway leaders, United, who had never previously won in Swansea, should have been a goal down inside four minutes.
Sadly, just as he had at Anfield two weeks previously, Gower wasted a glorious chance from 20 yards.
The hosts were made to pay for that miss, barely four minutes later. Ryan Giggs picked up Angel Rangel's careless pass on the edge of his own box, and Hernandez converted the Welshman's cross at the near post.
It took the sting out of Swansea and the crowd too. A full house attendance had arrived in hope of seeing the Swans extend their unbeaten run on home soil this season.
To their credit they continued to play the kind of expansive football that has endeared them to so many in recent seasons.
Unfortunately, they came up against a United side that begin to grow in confidence on the back of Hernandez' goal.
Rooney and Giggs pulled the strings in midfield with Nani and Park Ji-Sung causing problems out wide. The only missing ingredient was a second goal.
To their credit, Swansea should have been level in the 22nd minute. Wayne Routledge presented Sinclair with an open goal, but with David De Gea stranded, the former Chelsea man missed from barely half a dozen yards.
Buoyed by that, Swansea enjoyed their fair share of possession with Nathan Dyer having a spirited tussle with Patrice Evra.
In the final minute of the first half, Rooney and Hernandez exposed Swansea down the left and should have done better with only Michel Vorm to beat.
Thankfully, for Swansea, Hernandez failed to find Rooney at the far post and the ball disappeared to safety.
Evra's rash tackle on Dyer, a minute into the second half, earned the full back a deserved booking. A minute later, Taylor's shot was beaten away by De Gea after excellent work from Dyer on the right.
The introduction of Joe Allen at half time had given Swansea far more bite in midfield and though United had been dominant for much of the game, they were suddenly under the cosh.
Successive corners from Sinclair caused further difficulties for the visitors and Garry Monk's far post header was diverted behind by Giggs.
Sinclair then wasted a golden chance to put Dyer through on goal and as United struggled to contain Swansea's five man midfield, Sir Alex Ferguson introduced Darren Fletcher.
Swansea continued to battle relentlessly, but were fortunate to survive when Rooney escaped the clutches of Monk and attempted the most audacious chip over the advancing Vorm. The Dutch keeper looked on helplessly as the ball landed on the top of his net.
Two minutes later and with Swansea now a spent force, Phil Jones broke into the City box and duly struck an upright with a shot that left Vorm rooted to his spot.