The Swans' interest in the FA Cup ended at the third-round stage after Jack Wilshere's 86th-minute strike settled this replay at the Emirates.
Arsenal put the Swans under considerable pressure throughout, with Danny Graham, Leon Britton and Dwight Tiendalli - on two occasions - clearing off the line while the hosts also struck the post.
Michel Vorm was in inspired form, denying the Gunners attack on several occasions.
The Swans' best effort came through ex-Arsenal centre-back Kyle Bartley, who saw his first-half header rebound out off the crossbar while Chico Flores saw his own header hit the sidenetting.
The second half was almost all Arsenal, and it took until four minutes from time for Wilshere to hammer home a thunderous effort and end the Swans' seven-match unbeaten run and FA Cup hopes.
The Swans made six changes. With Ashley Williams and Angel Rangel rested, in went Jazz Richards - who made his fourth appearance this season - and Kyle Bartley, who left the Gunners last summer to head to the Liberty, in the two changes at the back while Leon Britton skippered the side against the club where he started his career.
Jonathan de Guzman was also back in the starting XI after coming off the bench at Everton while Wayne Routledge and Danny Graham were also recalled to the starting XI.
Arsenal: Wojciech Szczesny, Abou Diaby (Aaron Ramsey, 84), Bacary Sagna, Per Mertesacker, Thomas Vermaelen (capt), Jack Wilshere, Olivier Giroud, Theo Walcott, Santi Cazorla, Francis Coquelin, Kieran Gibbs.
Subs: Vito Mannone, Lukas Podolski, Andre Santos, Alex Oxlade-Chamberlain, Andrey Arshavin, Carl Jenkinson.
Swans: Michel Vorm, Jazz Richards, Chico Flores, Kyle Bartley, Dwight Tiendalli, Leon Britton (capt), Kemy Agustien (Pablo Hernandez, 61), Jonathan de Guzman (Ki Sung-Yueng, 62), Nathan Dyer, Wayne Routledge, Danny Graham (Michu, 72).
Subs: Gerhard Tremmel, Garry Monk, Ben Davies, Itay Shechter.
The hosts made a bright start, Olivier Giroud heading over before steering Theo Walcott's low cross wide with Michel Vorm untroubled.
The Swans responded with a neat passing move involving Dwight Tiendalli, Wayne Routledge and Nathan Dyer, with the latter eventually seeing his shot blocked.
Danny Graham then scuffed a 20-yard effort wide after Jonathan de Guzman pinched possession off Abou Diaby, before Kieran Gibbs' low effort following a clearance from a Jack Wilshere corner was saved low down by Vorm.
The Swans then went within inches of opening the scoring, de Guzman's curling cross met by the head of Kyle Bartley, who beat Wojciech Szczesny but not the crossbar in a replica of his effort from the original tie at the Liberty.
Kemy Agustien then threaded through a fine pass for Dyer, who was denied by a well-timed challenge from Thomas Vermaelen 12 yards out.
Tiendalli then blocked out Giroud's powerful shot before Vorm reacted superbly to deny Vermaelen from eight yards out after Chico Flores' headed clearance dropped to the Belgian.
Half-time: Arsenal 0 Swans 0
The Gunners were quick out of the blocks in the second half, and Walcott went within inches of breaking the deadlock in the 49th minute as he latched onto Diaby's through ball, but his chip over Vorm bounced just past the far post.
Santi Cazorla then fired a thunderous strike just over the crossbar before Giroud hit a first-time volley across the face of goal.
The Frenchman then glanced Walcott's corner before Michael Laudrup made his first change, with Pablo Hernandez replacing Agustien just past the hour mark.
Another change quickly followed, Ki Sung-Yueng coming on in place of de Guzman.
Then the Swans had two huge scares, with Graham using his chest to deny Walcott from six yards before Britton headed off the line from Giroud following a corner.
Giroud was at it again, hitting a curling effort on the turn but Vorm collected, then Walcott directed his 15-yard shot wide as the hosts upped the pressure.
Laudrup then made his final change with 18 minutes to go as Michu replaced Graham.
Vorm denied Arsenal again, swatting away Wilshere's powerful drive before denying Giroud from close range.
The Swans kept plugging away, and Ki saw his low shot tipped wide for a corner by Szczesny. From the resulting delivery, Chico Flores dived low and his header crashed into the sidenetting.
The action didn't stop, and when Walcott failed to get onto the end of a cross, Vorm could only watch the ball bounce onto the post and into his hands.
Walcott was then kept out again by Vorm, before the Dutchman flew across goal to palm out a dangerous cross to the back post.
Arsenal were sensing the opener would come, and Giroud twice went close with a header and volley but was blocked on both occasions by Tiendalli.
But Arsenal did get their goal, four minutes from time as Wilshere finally found a way past Vorm, getting onto the end of Giroud's neat touch and blasting into the bottom corner.
And that proved the last real action, with Arsenal comfortably seeing out the rest of the game to advance to the fourth round and book a trip to Brighton.