Garry Monk's side completed a shock 1-0 win to dent the Gunners' hopes of finishing second in the Barclays Premier League at the Emirates Stadium last night.
Arsenal dominated the game at the Emirates Stadium and created a number of excellent chances in the second half but it was the visitors who grabbed a late winner after Bafetimbi Gomis's 85th-minute header was ruled to have crossed the line by the goal decision system.
The visitors held on through the four minutes of stoppage time - despite being put under pressure by Arsenal - for their third successive win, one which leaves them just one point behind seventh-placed Southampton with two matches remaining.
Seventh place would be enough for Europa League qualification for Swansea should Arsenal beat Aston Villa in the FA Cup final on May 30.
Swans boss Monk said he was not focusing on Europe yet, but would see how the last two games of the season pan out.
I don't focus on that. What will be will be and we'll just keep pushing.
I said that before the the game, over the weekend, the good thing about playing on Monday night was that we saw the results and that the places above us had opened up with the results, so why shouldn't we be pushing for that? Why shouldn't we be pushing those teams above and go on the hunt for them.
I think today showed exactly what we're about and how we think about each game and we'll take the next two games and whether that takes us, then great... if not we'll have to assess again in the summer.
Swansea City have beaten Arsenal 1-0 at the Emirates Stadium.
It was quiet first half with neither team managing to put any points on the board.
The second half was much of the same heading into the 85th minute goalless, but a late header by Bafetimbi Gomis saw the Swans take the win.
Swansea City beat Stoke City 2-0 to move closer to their best-ever Premier League finish.
Garry Monk's side secured a hard-fought victory, with two goals in the last 15 minutes at the Liberty Stadium.
Winger Jefferson Montero and midfielder Ki Sung-yueng scored, while Marc Wilson was sent off for the visitors.
The result means Swansea are eighth in the league, six points ahead of both West Ham and Stoke, with three games of the season remaining.
Swansea City's clash with Leicester at the King Power Stadium has ended in a 2-0 defeat this afternoon.
Despite Swansea's attempts to rally in the second half, with notable attempts from Jonjo Shelvey and Nelson Oliveira, it was another disappointing match for Garry Monk's side.
Swansea manager Garry Monk says he takes speculation linking him to replacing Sam Allardyce at West Ham as a compliment.Read the full story ›
Swansea City full back Kyle Naughton will miss the rest of the season after damaging ankle ligaments during his side's 3-1 win over Hull on Saturday.
Naughton, who joined the Swans in January from Tottenham Hotspur, was carried off in the second half after David Meyler's tackle which saw the Hull player sent off by referee Andrew Marriner.
Initial investigations ruled out a break but further scans have show significant ligament damage which will keep Naughton out for around six weeks.
Swansea City manager Garry Monk praised Bafetimbi Gomis following yesterday's 3-0 win over Hull.Read the full story ›
Swansea City midfielder Tom Carroll is facing up to six weeks on the sidelines with ankle ligament damage.
The England Under-21 International was hurt during their 1-0 victory over the Czech Republic last Friday, in which he scored their only goal.
A spokesman for Swansea City confirmed the 22-year-old is now expected to be out for between four and six weeks.
So far Carroll has made 18 appearances for the Swans, after joining them last summer on a season-long loan.
Elsewhere it's understood manager Garry Monk is awaiting results of a scan on winger Jefferson Montero, who reportedly suffered a muscle strain last weekend.
The Swans continue their Premier League campaign on Saturday, when they host Hull City.
Swansea City have beaten Aston Villa away in the Premier League after a late goal from Bafetimbi Gomis.
It was goalless for much of the game until the 87th minute when Gomis broke the deadlock after a cross from Jefferson Montero.
Swansea move to eighth position in the Premier League.
It's level at Villa Park this afternoon as Swansea take on Aston Villa in the Premier League.