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The Swans suffered a second consecutive Barclays Premier League defeat as second-half goals from Nacho Monreal and sub Gervinho kept Arsenal's hopes of Champions League qualification alive.
The Gunners had struck the crossbar twice in the first half through Alex Oxlade-Chamberlain, while Michu and Angel Rangel went close for the Swans in a bright first period.
But the visitors claimed their first win at the Liberty when Monreal gave them the lead with 15 minutes to go after he struck past Michel Vorm in a crowded area.
And Arsenal wrapped up the win in added on time as Gervinho found himself unmarked from 12 yards following a counter attack, and he slotted past the Dutch keeper to give Arsene Wenger's side the three points.
Michael Laudrup made two changes from his starting XI. Leon Britton has recovered from the hip injury which saw him sit out the defeat at West Brom, so he returns in place of Wayne Routledge, who drops to the bench.
Michu led the line up front, which meant Luke Moore - who had two goals in his last two appearances - was among the replacements as Nathan Dyer went back in the starting line-up.
Swans: Michel Vorm, Angel Rangel, Garry Monk (capt), Ashley Williams, Ben Davies, Leon Britton, Ki Sung-Yueng (Wayne Routledge, 66), Jonathan de Guzman, Nathan Dyer (Luke Moore, 76), Pablo Hernandez, Michu.
Subs: Gerhard Tremmel, Dwight Tiendalli, Kyle Bartley, Roland Lamah, Itay Shechter.
Arsenal: Lukasz Fabianski, Abou Diaby (Aaron Ramsey, 71), Per Mertesacker, Laurent Koscielny, Mikel Arteta (capt), Olivier Giroud, Theo Walcott (Kieran Gibbs, 85), Alex Oxlade-Chamberlain (Gervinho, 71), Nacho Monreal, Santi Cazorla, Carl Jenkinson.
Subs: Wojciech Szczesny, Thomas Vermaelen, Tomos Rosicky, Francis Coquelin.
On a slick surface at the Liberty, it was the Swans who threatened first as Pablo Hernandez found Nathan Dyer on the edge of the box after three minutes, but he curled his effort high and wide.
Arsenal immediately replied as they went within inches of opening the scoring. Alex Oxlade-Chamberlain got the kind deflection after a challenge from Angel Rangel, and the winger cut inside before unleashing a powerful shot which cannoned off the crossbar.
Rangel was in the action at the other end, getting onto the end of Ki Sung-Yueng's pass through the visitors' defence but the Spaniard sliced his effort wide from just inside the box.
Michu then volleyed into the ground after Ben Davies curled in a cross before the striker went close again soon after, collecting Jonathan de Guzman's pass before his shot on the turn bounced just past the post.
Michel Vorm then had to push Santi Cazorla's powerful volley into the air before collecting again, as the game continued to produce chances.
Ashley Williams put his body on the line to deflect Theo Walcott's shot wide for a corner before the Gunners struck the crossbar for the second time in the half.
Oxlade-Chamberlain had a yard of space before his thunderous shot beat Vorm but not the woodwork as it clipped the top of the crossbar.
That was the end of the action in the first half, which promised more after the break.
Half-time: Swans 0 Arsenal 0
Neither manager made a change at the break as both sides looked for an opening goal.
Cazorla drove low at goal five minutes into the half, which Vorm did well to gather after a bounce, then Michu fired Hernandez's square pass high into the stands.
Hernandez then tried his luck after evading both Carl Jenkinson and Abou Diaby, but his curling effort flew yards wide with Lukasz Fabianski untroubled.
The game ticked past the hour mark before Michael Laudrup made his first change, Wayne Routledge replacing Ki.
Arsene Wenger made a double change of his own, Gervinho replacing Oxlade-Chamberlain and Aaron Ramsey taking the place of Diaby.
It paid off for the visitors as they took the lead four minutes later, Olivier Giroud touching down to Nacho Monreal after Cazorla's mazy run, and the left-back squeezed his effort through a crowded box and past Vorm.
The Swans were looking for an instant response, Luke Moore replacing Dyer in another change by Laudrup, and de Guzman curled a 25-yard free-kick into the sidenetting as the game entered the last five minutes.
Cazorla nearly settled the contest late on, his effort deflected just wide for a corner.
But the Gunners did wrap it up in added on time. With the Swans pushing up in search of an equaliser, the visitors raced on a counter attack and Ramsey fed the unmarked Gervinho, who slotted past Vorm from 12 yards.