Scorers: Swansea - Bony (14), Michu (58), de Guzman (62)
Referee: S Gumienny
The home side were forced to play 80 minutes with ten men after defender Adil Rami saw red for hauling down Wilfried Bony. The striker went on to give Swansea the lead in the 14th minute with his fifth goal in eight games, firing home with the help of a deflection.
Michu and a wonderful Jonathan de Guzman free-kick completed the scoring in the second half as the Swans cruised to victory at a stunned Mestalla.
There have been more important victories in Swansea’s 101 years, but there will have been few as eye-catching as this, adding another remarkable chapter to their remarkable rise from League Two to the Premier League, Capital One Cup glory and this European campaign.
Valencia, two-time Champions League finalists, were in trouble from the moment Rami saw red. Bony threatened to race clear of the Frenchman, and the referee quickly had the card out of his pocket as Bony went to ground.
The Ivory Coast international got the opener shortly after as Alejando Pozuelo and Michu combined for him to rifle home.
Pozuelo, an exciting presence throughout, was involved again when his excellent pass teed up Michu for the second in the 58th minute. And De Guzman rounded matters off with a spectacular strike four minutes later to leave the Welsh club in dreamland.
Valencia are the top seeds in Group A, and the competition – although they are in the midst of their worst run in 14 years. But even the most optimistic Swansea fan could not have anticipated such a great start.
They survived an early scare when Sergio Canales escaped Chico Flores and produced an excellent ball that Sofiane Feghouli just failed to get a touch on.
But the Welsh side, fielding more Spanish players than their hosts, took control after Valencia were reduced to ten men with less than ten minutes on the clock.
Rami dragged back Bony as the striker got away from him 30 yards from goal. The French international had team-mates near but Belgian referee Serge Gumienny did not hesitate as he produced a red card.
Los Che boss Miroslav Djukic was forced to sacrifice Fede Cartabia to get defender Ricardo Costa on, but seconds after the change his side conceded.
Pozuelo fed Michu on the left, and when his pull-back ran through to Bony the striker dispatched a left-footed strike high into the net with the aid of a deflection off Ever Banega.
Costa almost gifted Swansea a second seven minutes later. His attempts to evade Pozuelo saw him only manage to deliver the ball to the feet of Nathan Dyer, but the winger failed to make the most of the chance as he dragged a shot wastefully wide.
Swansea were in complete control, dominating possession as their numerically disadvantaged hosts toiled. Bony’s power was providing them with a particular headache, and the Ivorian almost got his second of the night five minutes before the break, getting the better of Costa before fizzing a shot just wide.
The half-time whistle was greeted with boos from the home fans and white hankies for the under-fire Djukic. Some had seen enough, with the lower tier behind one of the goals, which had been full, slowly emptying as the teams returned to the field as part of a planned protest, before the fans reclaimed their seats around ten minutes into the second period.
In that time, Swansea missed two gilt-edged chances, Bony heading over from close range while Michu volleyed over when unmarked.
When the supporters did return, they were just in time for Swansea’s second goal. De Guzman laid the ball off to the lively Pozuelo and his lovely pass afforded Michu the room to fire home with his right foot.
It was soon 3-0. Pozuelo was fouled by Banega 30 yards out, and De Guzman’s curling, dipping free-kick beat Vicente Guaita all ends up, handing Swansea just a second ever away win in European competition.
Valencia: Guaita, Barragan, Rami, Feghouli (Pabon 59), Mathieu, Ever, Javi Fuego, Guardado, Canales (Bernat 66), Cartabia (Ricardo Costa 14), Postiga. Subs Not Used: Diego Alves, Jonas, Alcacer, Parejo.
Swansea: Vorm, Rangel (Ben Davies 55), Amat, Chico, Tiendalli, de Guzman, Canas, Pozuelo, Dyer (Lamah 65), Michu (Shelvey 76),Bony. Subs Not Used: Tremmel, Routledge, Monk, Vazquez.