An 89th minute own goal earned the Swans a deserved draw at the Emirates in what could prove a vital point come the end of the season.
Garry Monk's side had taken an 11th minute lead as Wilfried Bony headed home Neil Taylor's cross for his 20th goal of the campaign.
The Swans had to defend resolutely, with captain Ashley Williams making a number of key blocks in the heart of the visitors' defence as Arsenal piled on the pressure.
The pressure finally told in the second half with the Gunners finding the net twice in as many minutes.
Firstly, substitute Lukas Podolski tapped home following some fine work by Kieran Gibbs and then Podolski turned provider a minute later as his cross found Olivier Giroud, who fired in from close range.
With the Swans heading for an undeserved defeat, the 2,000-strong Jack Army were on their feet celebrating with just a minute left of normal time.
Leon Britton's surge into the box was ended by a Per Mertesacker challenge, but the ball bounced off Wojciech Szczesny and then Mathieu Flamini before trickling over the line.
The Swans then went in search of a winner, and in the fourth minute of added on time, sub Pablo Hernandez's through ball sent Jonathan de Guzman racing forward on the halfway line with the Arsenal defence behind him.
But referee Lee Probert called time on the match, with the Swans having to make do with a point.
It is a point which takes them onto 30 points from 31 games - five points clear of third-bottom Sunderland - with Norwich City next up at the Liberty on Saturday.
The Swans made four changes to the starting XI.
Following Saturday's 3-2 defeat at Everton, Neil Taylor started at left-back while Jonjo Shelvey came into midfield with Jonathan de Guzman given a chance out wide on the right.
The final changes saw Spanish international Michu make his first start since December 15 as he completed his full return from an ankle injury.
ARSENAL: Wojciech Szczesny, Bacary Sagna, Per Mertesacker, Thomas Vermaelen (capt), Kieran Gibbs, Mathieu Flamini, Mikel Arteta, Alex Oxlade-Chamberlain (Lukas Podolski, 57), Tomas Rosicky (Kim Kallstrom, 79), Santi Cazorla, Olivier Giroud (Yaya Sanogo, 87).
SUBS: Lukasz Fabianski, Carl Jenkinson, Hector Bellerin, Serge Gnabry.
SWANS: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Neil Taylor (Ben Davies, 74), Leon Britton, Jonjo Shelvey (Pablo Hernandez, 79), Michu (Nathan Dyer, 63), Jonathan de Guzman, Wayne Routledge, Wilfried Bony.
SUBS: Gerhard Tremmel, Jordi Amat, Jose Canas, Alvaro Vazquez.
After Arsenal made an early threat through Alex Oxlade-Chamberlain, who was denied by Michel Vorm, the Swans stunned the Emirates into silence.
With 11 minutes on the clock, the Swans worked possession around the park, and when Neil Taylor raced down the left, his pinpoint cross was met by Wilfried Bony, who beat Thomas Vermaelen to head into the corner of the net for his 20th goal of the season.
Arsenal looked for an instant reply, and they almost got one as Per Mertesacker got onto the end of Santi Cazorla's corner, but the big German's header dropped into the sidenetting.
Then Oxlade-Chamberlain was the next to find the sidenetting after his quick pace earned him a yard of space inside the Swans box.
Arsenal were enjoying the possession and territory, but the Swans were defending resolutely with Bony's defensive headed clearances proving invaluable while captain Ashley Williams led by example with a number of key challenges and blocks.
With the clock ticking towards the break, Arsenal upped the pressure, and Vorm had to be alert to swat away Cazorla's driven effort.
But the Swans had done enough to protect their lead as they went into half-time with a precious 1-0 lead.
HALF-TIME: Arsenal 0 Swans 1
The Swans again had to cope with some heavy Arsenal pressure, but they were looking dangerous on the counter attack with Michu firing wide after some neat link-up play from Bony and Jonathan de Guzman.
Arsenal were finding it hard to break down the Swans backline and Tomas Rosicky's 25-yard effort, which flew high and wide, was the best they created as the game passed the hour mark.
The Swans kept plugging away though, and after Jonjo Shelvey saw his 30-yard strike land yards wide, the visitors soon created another opportunity but Michu couldn't get his header on target following a de Guzman cross.
Garry Monk made his first change in the 63rd minute as Nathan Dyer replaced Michu, which saw de Guzman move into central midfield.
It was tense stuff at the Emirates with the home fans cheering on their side in hope of a goal, with the 2,000-strong Jack Army backing the Swans.
And the home crowd got what they wanted with two goals in as many minutes.
With 73 minutes gone, Kieran Gibbs raced into the box and he perfectly picked out sub Lukas Podolski, who tapped home from two yards.
And just 60 seconds later the Emirates was in ecstasy as Podolski turned provider with his excellent low cross finding Olivier Giroud, and he also tapped home from two yards.
It was harsh on the Swans, but they still had time to get themselves back onto level terms.
Bony, a constant threat to the home defence, appeared to be barged off the ball inside the box as a de Guzman free-kick was being delivered, but referee Lee Probert waved away the protests.
The Ivorian was again in the centre of the action soon after he rose to meet sub Pablo Hernandez's cross, but it landed straight into Wojciech Szczesny's hands.
Then, with a minute to go, the Swans silenced the Emirates as they got back onto level terms.
Leon Britton's scything run saw him latch onto Rangel's superb flicked pass inside the box and when the midfielder was beaten to the ball by Mertesacker's challenge, the ball deflected off Szczesny and onto the boot of Flamini and into the net.
It was sensational stuff, but there was a tense finale to come.
And it was a controversial one at that, with the Swans catching Arsenal off guard as Hernandez's penetrative pass sending de Guzman with a race towards goal from the halfway line.
But as the Dutchman started his long trek towards a potential winner, referee Probert blew the final whistle.