The Swans were denied a famous Europa League win as Napoli held out in a hugely entertaining 0-0 draw at the Liberty.
Garry Monk's side enjoyed almost total domination against the Italian side, who host the last 32 second leg tie in Naples in a week's time.
The Swans had almost 70 per cent of possession in this thrilling encounter, with 21 shots on goal against a side that had only dropped into this competition via goal difference in the Champions League.
But they couldn't break through Rafa Benitez's solid side, with keeper Rafael Cabral - who was replaced through injury at half-time - and substitute Pepe Reina making a string of fantastic saves.
The best chances of the game fell to Wilfried Bony, who was denied by Cabral's chin when put in on goal by a brilliant Pablo Hernandez pass.
And Ashley Williams was denied at the back post by Reina after the skipper met a Jonathan de Guzman free-kick.
But the Swans will head to the Stadio San Paulo in seven days' time hugely encouraged by this performance as they look to continue their fantastic European adventure.
First up, though, for Monk and co is a trip to Liverpool on Sunday in the Barclays Premier League.
The Swans made eight changes to the starting XI.
From the FA Cup defeat to Everton, Garry Monk changed his entire back five for this first leg tie as Michel Vorm returned between the sticks, with skipper Ashley Williams and Chico Flores partnered in the heart of defence and Angel Rangel and Ben Davies either side of them.
Leon Britton was back in midfield and Nathan Dyer started on the wing while club-record signing Wilfried Bony led the line.
On the bench, Jonjo Shelvey was included for the first time since the league defeat to West Ham on February 1.
SWANS:Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Jose Canas (Jonjo Shelvey, 71), Pablo Hernandez (Jonathan de Guzman, 56), Nathan Dyer (Marvin Emnes, 78), Wayne Routledge, Wilfried Bony.
SUBS: Gerhard Tremmel, Jordi Amat, Neil Taylor, David Ngog.
NAPOLI: Rafael Cabral (Pepe Reina, ht), Anthony Reveillere, Henrique, Miguel Britos, Jose Callejon, Gonzalo Higuain (Goran Pandev, 83), Christian Maggio, Marek Hamsik (capt), Blerim Dzemaili, Lorenzo Insigne (Dries Martens, 74), Gokhan Inler.
SUBS: Faouzi Ghoulam, Raul Albiol, Valon Behrami, Duvan Zapata.
The game got off to a pulsating start, with Jose Callejon firing wide after three minutes and then a swift Napoli counter attack led to skipper Marek Hamsik racing on and shooting for goal, but a superb reflex save from Michel Vorm tipped it wide for a corner.
At the other end, it took another fantastic save - this time from Rafael Cabral - as the Napoli keeper swatted Nathan Dyer's first-time curling effort wide for a corner after the winger had latched onto Pablo Hernandez's return pass.
The Swans were looking dangerous going forward, and Dyer in particular was causing problems to the visiting defence with his pace.
And the winger was at it again with 17 minutes gone. He left Anthony Reveillere behind as he raced down the right flank, but his cross just evaded the head of Bony.
Then it was the turn of Hernandez to inject some magnificence as his finely-threaded pass sent Bony in on goal, but the Ivorian's shot cannoned off the chin of keeper Cabral and out for a corner.
Bony was at it again just past the half-hour mark as Routledge, following some excellent hold up play down the left, crossed to Hernandez, and when the Spaniard's chip back into the face of goal reached Bony, the striker climbed highest but could only direct his header straight into the hands of Cabral.
The Swans continued to press, and next to try his luck was Jose Canas, who intercepted a pass before chesting and volleying just over the crossbar from 20 yards out.
The chances kept coming, and Ashley Williams should have made more of his header after he was found by Hernandez, but the skipper's attempt landed over the crossbar.
Garry Monk's side were piling on the pressure, and another chance saw Routledge cut inside before unleashing a rising effort which Cabral tipped over for a corner.
The visitors' keeper was at his best from the resulting delivery, swatting Angel Rangel's back-post header over for another corner as the game entered the final moments of the half.
The Swans, though, went into the break without a goal but would have been hugely satisfied with their first-half performance.
HALF-TIME: Swans 0 Napoli 0
Napoli were forced into a change at the break as Pepe Reina replaced keeper Cabral, who suffered an injury in the final seconds of the first half.
And it wasn't long before the Swans were looking to test the Spanish international, but Hernandez's shot was deflected wide.
But, as a reminder of their danger on the counter, skipper Hamsik picked out Gonzalo Higuain but the Argentinian volleyed high and wide from just inside the box.
Then Hernandez waltzed his way into the Napoli box, but again his shot was blocked out.
It proved the Spaniard's final say as he was replaced by Jonathan de Guzman.
The wave of pressure continued and Rangel was next to probe after a neat passing move involving de Guzman and Routledge, but his shot was way off target.
Napoli replied with a rare venture forward, this time Callejon nutmegging Ben Davies before skewing his shot well wide.
But the home side were quickly back on the attack, and it took a fantastic reflex save from Reina to deny Williams from heading home following de Guzman's free-kick.
Another change was made by Monk as Jonjo Shelvey came on in place of Canas as the Swans threw on more of an attacking option.
And Shelvey was soon in the centre of the action as he teed up Routledge to shoot, but Reina dived to palm his effort int the patch of Dyer, but after seeing his volley bounce wide the winger was replaced by Marvin Emnes after sustaining an injury.
The game entered the final ten minutes with the Swans pushing hard for the game's first goal.
And Bony, a constant menace to the Napoli defence, again probed as leapt to meet a deflected Rangel cross but Reina watched motionlessly as the ball dropped past his near post.
A minute later Reina was again called into action as Chico Flores beat the offside trap to latch onto de Guzman's curling free-kick, but the defender's header dropped straight into the replacement keeper's hands.
Four minutes of added on time was to follow, and the passionate home crowd continued to cheer on the Swans.
But Napoli held on to claim a draw, though the Swans will be massively encouraged by their performance.