Michael Laudrup made four changes to the side that drew with Aston Villa on New Year's Day as Kyle Bartley made only his second start of the season to partner Chico Flores in defence, with Ashley Williams being rested.
Dutch full back Dwight Tiendalli and Nathan Dyer also returned to the side, with Angel Rangel and Pablo Hernandez dropping to the substitutes bench.
Top scorer Michu was also among the subs, with Ki-Sung Yueng coming in to partner Jonathan de Guzman and Leon Britton in midfield.
Meanwhile, Arsenal made three changes to the side that drew with Southampton as Per Mertesacker replaced captain Thomas Vermaelen, while Aaron Ramsey and Olivier Giroud were preferred to Alex Oxlade-Chamberlain and Lukas Podolski.
Michel Vorm, Dwight Tiendalli, Chico Flores, Kyle Bartley, Ben Davies, Leon Britton (Kemy Agustien, 69), Ki Sung-Yueng, Jonathan de Guzman (Michu, 57), Wayne Routledge (Pablo Hernandez, 57), Nathan Dyer, Danny Graham.
Gerhard Tremmel (gk), Garry Monk, Angel Rangel, Kemy Agustien, Pablo Hernandez, Itay Shechter, Michu.
Wojciech Szczesny, Bacary Sagna, Per Mertesacker, Laurent Koscielny, Keiran Gibbs, Mikel Arteta (capt), Jack Wilshere, Aaron Ramsey (Lukas Podolski, 72), Santi Cazorla, Olivier Giroud, Theo Walcott.
Damian Martinez (gk), Thomas Vermaelen, Andre Santos, Francis Coquelin, Tomas Rosicky, Alex Oxlade-Chamberlain, Lukas Podolski.
After a quiet opening in which Arsenal dominated possession, it was the Swans who created the game's first chance as Danny Graham latched onto a wonderful pass from Kyle Bartley before firing off a shot that Wojciech Szczesny did well to parry away.
The visitors responded with a chance of their own on 20 minutes as in-form Theo Walcott found a yard of space in the box, but his curling effort was headed clear by Bartley.
Then, on the half hour mark, Aaron Ramsey jinked his way into the penalty and just as the former Cardiff man looked destined to give Arsenal the lead, Ben Davies came across with a wonderful saving challenge to deny him.
The Gunners continued to press and they had their best opening of the half just three minutes later as Keiran Gibbs surged down the left edge of the box and as he pulled the ball back to Santi Cazorla the Spaniard fired high over the bar.
At the other end, the Swans came close again as Jonathan de Guzman’s free kick was met by Kyle Bartley, but the former Arsenal man saw his header come back off the crossbar with Szczesny beaten.
The last action of the half saw Cazorla fire in a snap shot at goal that was comfortably saved by Vorm.
Half time: Swans 0 Arsenal 0
Arsenal began the second half with renewed vigour and came close to breaking the deadlock within five minutes as Walcott fed Giroud, but the Frenchman's fierce drive was beaten away by Vorm.
The visitors then had a penalty appeal turned down as Ramsey hit the deck under pressure from Tiendalli, before Vorm was called into action once more as he saved smart from Giroud's acrobatic effort.
The Swans were on the back foot and Michael Laudrup responded by making a double substitution.
Jonathan de Guzman and Wayne Routledge made way for Pablo Hernandez and Michu as the home side looked to force their way back into an open contest.
And it proved to be an inspired change as the home side took the lead on 58 minutes.
Michu - who had been on the field less than a minute - flicked the ball over the head of Per Mertesacker before bearing down on goal and coolly tucking the ball past Szczesny.
Arsenal responded with Giroud heading wide from six yards out after good work from Ramsey down the left, before Jack Wilshere shot well wide from 25 yards out.
The Swans then made their final change of the afternoon as Leon Britton made way for Kemy Agustien, handing the captain's armband to Michel Vorm.
Arsenal made a change of their own with just under twenty minutes to play as Aaron Ramsey was replaced by Lukas Podolski.
And they came close to an equaliser with 75 minutes on the clock as a wayward pass found its way to Walcott inside the box and the England international found half a yard before shooting inches wide of Vorm's right hand post.
But Arsene Wenger's men continued to press and they got their reward with ten minutes to play.
After Theo Waclott's far post corner found Sagna, the ball came back into the box and Podolski was on hand to fire an unstoppable left foot shot into the bottom corner.
And the travelling Arsenal fans were on their feet once more just two minutes later as the visitors took the lead.
Following neat interchange on the left corner of the box, Giroud clipped a ball into the path of Keiran Gibbs and the defender smashed a superb volley into the roof of the net.
However, and not for the first time this season, the Swans roared back and levelled the contest with three minutes to play.
After Kemy Agustien's corner wasn't cleared by the Arsenal defence, Ki Sung-Yueng set up Danny Graham six yards out and the striker lashed the ball past Szczesny and into the top corner.
There was still time for both sides to come close to a winner though, as Laurent Koscielny saw a header superbly saved by Vorm before Dwight Tiendalli saw an effort hit the sidenetting at the other end.
But it finished honours even, with a replay at the Emirates required to separate the two sides.