Wilfried Bony opened the scoring in the Group A encounter with his fourth goal in four European fixtures this season, before Michu and Jonathan de Guzman completed the comfortable victory in the second half.
Valencia's night started poorly when Adil Rami was sent off for bringing down Bony in the early stages, and the Ivorian opened the scoring with a powerful effort shortly after.
Michu deservedly grabbed a second with a driven strike inside the box, before De Guzman's stunning free-kick from distance ensured the victory.
Swansea boss Michael Laudrup made five changes to the side that drew 2-2 with Premier League leaders Liverpool on Monday, with the likes of De Guzman and Alejandro Pozuelo winning recalls.
Valencia slumped to a 3-1 defeat at Real Betis on Sunday – their third La Liga defeat in a row – and as a result manager Miroslav Djukic dropped Joao Pereira and Juan Bernat, with defenders Antonio Barragan and Andres Guardado selected in their place.
Swansea made a bright start to the match and received a boost in the 10th minute when Valencia defender Rami was given his marching orders.
The lively Bony pounced on a mistake from Ever Banega and raced clear of Rami, only to be hauled down by the France international.
Djukic was forced to shuffle his pack as a result, introducing another central defender, Ricardo Costa, in place of Federico Cartabia.
But the change could not stopping Swansea taking the lead as Bony put the visitors ahead in the 14th minute.
Neat interplay between Michu and Pozuelo led to the former centring for Bony from the left and he hit a fierce left-foot strike from just inside the area that whistled past Valencia goalkeeper Vicente Guaita.
Costa then nearly gifted Swansea a second when his attempted clearance was played straight to Nathan Dyer, but the winger, who raced clear, dragged his shot wide.
Bony came agonisingly close to a second five minutes before half-time when he turned Costa easily before flashing an effort narrowly wide.
Swansea started the second period in similar fashion and twice Bony missed good opportunities to double their advantage.
But the away side deservedly grabbed a second in the 58th minute.
Pozuelo collected a De Guzman pass before playing a perfectly weighted pass to Michu on the right hand side of the box and the forward rifled home at the near post.
De Guzman then produced a moment of sheer brilliance just four minutes later.
Banega conceded a soft free-kick 30 yards from goal on the left and the Netherlands international bent a superb strike into the top corner to delight the away fans.
With the game all but won Swansea slowed the tempo down, allowing Valencia to enjoy a spell of possession, and Helder Postiga almost grabbed a consolation with eight minutes remaining but headed Barragan's cross harmlessly wide.
Jonjo Shelvey also came close with an ambitious chip at the other end, but three goals were more than enough for an excellent Swansea side.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
