The Swans made a dream start to the Barclays Premier League season after beating Manchester United 2-1 at Old Trafford.
Ki Sung-Yueng gave Garry Monk's side a shock 28th-minute lead as his left-footed shot nestled into the bottom corner in what was his first goal for the club.
The hosts, led by Louis van Gaal for the first time, were level after the break as captain Wayne Rooney fired in from close range.
But Monk's men rallied again, and they stunned Old Trafford once again as summer signing Gylfi Sigurdsson saw his effort just manage to cross the line despite the efforts of David De Gea.
After an historic FA Cup victory at this ground last season, Monk's men then celebrated a first ever league win as the final whistle blew.
A dream result for the Swans, with Monk off to the perfect start in his first full season in charge.
Garry Monk made three changes from the side that lost to Villarreal.
Jordi Amat came into defence to partner skipper Ashley Williams, while Nathan Dyer returned to the starting line-up in place of Jefferson Montero, who was among the substitutes.
Wayne Routledge recovered from a minor foot injury as he took the place of Bafetimbi Gomis, with last season's top scorer Wilfried Bony leading the attack.
Lukasz Fabianski made his first Swansea City start in the league following his summer move from Arsenal.
MAN UTD:David de Gea, Phil Jones, Chris Smalling, Tyler Blackett, Jesse Lingard (Adnan Januzaj, 24), Darren Fletcher, Ander Herrera (Marouane Fellaini, 66), Ashley Young, Juan Mata, Wayne Rooney (capt), Javier Hernandez (Nani, ht).
SUBS: Ben Amos, Recce James, Michael Keane, Shinji Kagawa.
SWANS: Lukasz Fabianski, Angel Rangel, Ashley Williams (capt), Jordi Amat, Neil Taylor (Dwight Tiendalli, 54), Ki Sung-Yueng, Jonjo Shelvey, Wayne Routledge, Nathan Dyer (Jefferson Montero, 66, Gylfi Sigurdsson, Wilfried Bony (Bafetimbi Gomis, 78).
Gerhard Tremmel, Kyle Bartley, Jazz Richards, Josh Sheehan. SUBS:
The Swans settled themselves into the game early, and a few half chances went astray as Wayne Routledge failed to control a Jonjo Shelvey pass into the box while Gylfi Sigurdsson's dipping shot was well gathered by David De Gea.
Louis van Gaal was then forced into a substitution after 24 minutes as Jesse Lingard came off the worst in a challenge with Ashley Williams and he was replaced by Adnan Januzaj.
Manchester United's first real threat on goal came soon after as Phil Jones' cross-come-shot looked goalbound before Fabianski tipped it over for a corner.
But Old Trafford was stunned into silence, bar the 1,800 or so away fans, with 28 minutes on the clock.
Following good work by Nathan Dyer down the right, the Swans launched an attack and when Sigurdsson teed up Ki Sung-Yueng on the edge of the box, the South Korean fired into the bottom corner for his first Swansea City goal.
United were being urged on to push for an equaliser by the home support, but the Swans were holding firm defensively.
And Garry Monk's side reached the break with their lead in tact after a hugely impressive first-half performance.
HALF-TIME: Manchester United 0 Swans 1
The hosts made another change at the break, Nani coming on for Javier Hernandez, which meant Wayne Rooney moved up front.
And it was captain Wayne Rooney who made the big impact eight minutes into the half. After Jones flicked on Juan Mata's corner, Rooney's overhead kick from six yards found the net.
With Neil Taylor having picked up a booking shortly before, Monk made a change as Dwight Tiendalli came on for the Welsh international.
The home side were looking to make the most of their momentum, and a superbly-timed sliding challenge from Ashley Williams denied Rooney as he was about to shoot inside the box.
And Rooney was at the centre of the next big opportunity as his 20-yard free-kick curled over the wall before rebounding off the outside of the post.
Both teams then made changes, with Jefferson Montero making his Premier League debut in place of Dyer, while for the hosts Marouane Fellaini came on for Ander Herrera.
And Montero made an instant impact as, following a quickly-taken free-kick from Bony, Sigurdsson touched on for the Ecuadorian, and when his cross was volleyed back along the face of goal by Routledge, Sigurdsson's eight-yard effort just found its way over the line after 72 minutes.
Monk made his final change with 12 minutes to go, Bafetimbi Gomis replacing Bony in a straight swap.
And the Frenchman came close to making it 3-1 in the final ten minutes as, following a link-up with Sigurdsson, the substitute raced on into the box, but a well-timed Jones tackle snuffed out the danger.
The hosts then probed via Ashley Young, but his dipping shot was gathered by Fabianski at the far post.
Monk's men still had a lot to do, with wave after wave of United pressure coming their way.
But they stood strong through the four minutes of added on time - despite a penalty appeal from Januzaj after his cross struck Angel Rangel's arm - to claim three historic points.