The English League Cup holders, in their first season in European competition for 22 years, took advantage of defender Adil Rami's 10th-minute dismissal to run riot in the Group A clash at the Mestalla with goals from Wilfried Bony, Michu and Jonathan De Guzman.
The opening group stage matches also threw up another shock in Eindhoven where PSV, one of five teams in action who have previously won the UEFA Cup or Europa League, were beaten 2-0 by Bulgarian champions Ludogorets Razgrad in Group B.
Swansea's record signing Bony continued his prolific start after joining from Vitesse Arnhem in July for 12 million pounds ($19.27 million) with a powerful first-time finish from Michu's centre, just minutes after Valencia had been reduced to 10 men.
Ivorian international Bony, with four goals in Europe this season, was set to race clean through before last man Rami impeded his progress and was shown a straight red card.
Spaniard Michu, whose first campaign in English football yielded 18 Premier League goals last season, again displayed his clinical finishing by doubling Swansea's lead on 58 minutes from Alejandro Pozuelo's pass.
A woeful night for Valencia, who won the 2004 UEFA Cup and were beaten finalists in successive Champions League finals at the turn of the century, was capped when De Guzman curled in a delightful free kick from 30 metres.
PSV goalkeeper Jeroen Zoet's misplaced clearance on the hour handed Ludgorets the opening goal in Eindhoven.
Zoet rushed out to clear a long ball but found only Roman Bezjak who stroked it back into the empty net.
Phillip Cocu's side conceded a second goal on 74 minutes when Virgil Misidjan put away the rebound after his shot struck a post.
In other matches, Spaniard Jonathan Soriano hit a hat-trick for FC Salzburg as the Austrian league leaders thumped Sweden's Elfsborg 4-0 in Group C.
Fiorentina also eased to a 3-0 win at home to Pacos Ferreira in Group E and Rubin Kazan romped to a 5-2 Group D victory over Maribor in Slovenia.
Tottenham Hotspur, Lazio and Sevilla are among the clubs in action later on Thursday.
(Editing by Tony Jimenez)