Former Queens Park Rangers midfielder Dani Parejo netted the winning goal, sliding the ball home from 12 yards after the home side failed to clear a corner.
Read below to see how the action unfolded at the Liberty Stadium.
Hello, and welcome to Sports Mole's live coverage of the match between Swansea City and Valencia in the Europa League.
I won't waste any time - here is the team news from the Liberty Stadium.
SWANSEA CITY XI: Tremmel; Rangel, Chico, Amat, Taylor; Britton, Shelvey, Pozuelo, Dyer, Lamah; Bony
VALENCIA XI: Alves; Joao, Ruiz, Mathieu, Guardado; Romeu, Parejo, Feghouli, Canales, Bernat; Jonas
The two teams have made their way out onto the pitch at the Liberty Stadium. Valencia have already qualified for the knockout stages, but Swansea still require a point. Ideally, they need three points if they have hopes of topping Group A.
Swansea get us started.
In the reverse fixture, Swansea completely dominated the Spaniards, but that could be attributed to Valencia being reduced to 10 men early in that match. This should be a much more competitive encounter.
Both Swansea and Valencia have made a patient start to the game. Nathan Dyer was gifted a glimmer of an opening, but he was well snuffed out by the defence.
BOOKING! Angel Rangel has gone into the referee's notebook after deliberately handling the ball when Valencia attempted to break forward.
Fantastic play from Swansea. Shelvey played Lamah in down the left and after an accurate cross towards the near post, Bony powered a header just wide of the mark. Encouraging stuff from Michael Laudrup's side.
Both teams are employing a similar kind of style, but Swansea look slightly more direct, and that is paying dividends at the moment. Wilfried Bony caused the Valencia defence all kinds of problems in the first game, and he is doing the same again.
CHANCE! So close! Alves attempts to punch a corner clear, but his intervention goes straight at Bony, who sees his header go no more than a yard past the post. Huge let-off for the goalkeeper.
Valencia get their first sighting of goal, but Canales's shot was weak and Tremmel had no problem gathering the ball.
GOAL! Swansea City 0-1 Valencia (Parejo)
Valencia have slowly but surely eased into this match, and they now have the lead. Tremmel punched a corner away, but it came back instantly and Parejo was on hand to direct the ball into the bottom corner from 12 yards. It was a bit of a gift, but they all count.
That goal has failed to dampen the enthusiasm of the Swansea supporters. They are still fully behind their side, but they are less than impressed when Shelvey skies a long-range effort into the stands.
One player who is looking the part for Valencia is Oriol Romeu. The midfielder is currently on loan from Chelsea after a couple of serious injuries hindered his chances at Stamford Bridge.
The confidence is oozing through Parejo after that opener. He has just tried a low 30-yard strike, and Tremmel was forced to tip the ball wide for a corner. This has been good from the visitors.
Swansea are attempting to build a response to going behind, but Valencia look a lot more resolute than two months ago. The hosts are also missing Michu, who was outstanding back in September.
Dyer battles superbly to hustle the ball off Guardado to earn a free kick for his side. It's a good delivery, but the ball is cleared for a throw in by the corner flag.
SHOT! Jonas has been quiet for Valencia so far, but he nearly announces himself with a thundering strike from 25 yards. The ball appeared to be always clearing the crossbar, but it may have grazed the woodwork after swerving over the hand of Tremmel.
Huge blow for Swansea. Bony has pulled up holding his hamstring, and he has immediately made it known that he is unable to continue. Alvaro Vasquez has entered the action.
Vasquez is an able deputy for Bony, but he doesn't offer the same physical presence at the muscular Ivorian. Laudrup could be forced to tinker with his gameplan at half time.
DISALLOWED GOAL! That's an appalling decision from the assistant. Vasquez has the ball in the net after Alves saved from Shelvey, but the flag has gone up for offside. The Spaniard was well onside, and he is rightly incandescent about the decision.
HALF TIME: Swansea City 0-1 Valencia
The half-time whistle goes, and boos echo around the Liberty Stadium. The supporters know that their side should be level. Instead, they are 1-0 behind and face an uphill task in the second half.
Valencia lead the shot count by eight shots to six, while they have also had 53% of the ball. It hasn't been one-sided by any means, but the visitors are showing their European experience so far.
In the other match involving an English team, Wigan are currently being held by Zulte Waregem. Victory for the Latics would seal their progress through to the last 32.
Michael Laudrup has withdrawn Roland Lamah and replaced him with Jonathan de Guzman, who scored a memorable free kick at the Mestalla in September. What Swansea would give for another here tonight. We are back underway.
SHOT! Guardado lets fly with a stinging effort from 25 yards but it was straight at Tremmel, who gathered at the second opportunity.
CHANCE! Valencia should double their lead when Feghouli strides behind the Swansea defence, but after being pressurised by Tremmel, he dinked his attempt wide of the far post.
BOOKING! Ouch. Angel Rangel is fortunate to avoid injury when Guardado goes sliding in for the ball, but the Mexican is rightly handed a yellow card by the referee.
Jordi Amat and Jonas are both down after a nasty clash of heads. Jonas doesn't look too bad, but the Swansea defender has a cut on the back of his head.
Jordi Amat is ready to return, but he is being denied access back on the pitch because he hasn't got a replacement shirt with a number on.
This is ridiculous. He tries to come back on for a second time, but again, he isn't allowed because he has the wrong name on his shirt! Finally, the Swansea kitman sorts a shirt with the correct name, and the Spaniard is back.
Good work from Neil Taylor wins a corner for his side. The ball to the back post has three players waiting to connect, but it's Rangel who attacks the ball, heading it straight at Alves.
SUBSTITUTION! This is a nice sight. Pablo Hernandez is entering the fray after being dogged by injury for the majority of the season. Hernandez missed out on his return to his former club in September, but he is applauded onto the pitch by both sets of supporters.
SUBSTITUTION! It's Valencia's turn to make an alteration, bringing on the diminutive Piatti for Feghouli.
BOOKING! Parejo is the next man to go into the book after barging into Pozuelo. The caution count is slowly going up, but it hasn't been a dirty game.
Swansea are throwing men forward in an attempt to force an equaliser. After Rangel miscues a volley, De Guzman forced a save out of Alves, with Vasquez missing out on the rebound.
However, with the more men that Swansea throw forward, the more likely they are to concede, and Valencia nearly wrap up the game at the other end. The Spanish team broke in numbers, and after the ball arrived at the feet of Guardado, he curled a shot over the bar.
Swansea are enjoying long spells of possession, but Valencia have 10 men camped behind the ball, and it's proving almost impossible to create a significant chance.
Valencia have finally retrieved the ball off the home side, and rather than break forward, they are more than happy to keep hold of possession, much like Swansea do at home. Have Swansea got anything left?
BOOKING! Shelvey has been booked for a needless arm in the face of Piatti. I have no idea what he was trying to achieve there. Swansea were breaking forward, and the midfielder can count himself fortunate to still be on the pitch.
OFF THE LINE! Shelvey very nearly redeems himself! The midfielder's excellent delivery was brought down by Vasquez, but his effort on goal was cleared off the line! So unlucky.
There will be four minutes of added-on time.
Angel Rangel has gone off injured, but Swansea don't have any substitutes left.
Swansea are still pressing, but the ball has ended up in the hands of Alves. That could be that.
FULL TIME: Swansea City 0-1 Valencia
The full-time whistle goes, and Swansea City have fallen to a narrow defeat to Valencia. The hosts matched their more experienced opponents all of the way, but they will go into the final game of the group still requiring a point to secure their route into the knockout stages.
That will be all from Sports Mole tonight. Thank you for joining us for this evening's games. Goodbye for now.