It was a lucky victory for the Gunners whose goal came in the 40th minute when Swans keeper Michel Vorm was extremely careless with his release.
The Dutchman got onto Theo Walcott's attempt on the left side of the penalty area, taking possession under no immediate danger, but when he went to roll it out, he threw straight into the heels of defender Angel Rangel and Andrey Arshavin was on hand to control before slotting into an unguarded goal from an acute angle.
Arsenal should have taken an early lead when new signing Mikel Arteta played a perfect ball to the right for Aaron Ramsey but his sliding effort was wide of the mark when he really should have scored.
Swansea's Danny Graham forced a top-class save from Wojciech Szczesny in the 6th minute when he whipped goalward from the edge of the area about ten minutes before Walcott was desperately unlucky not to score with an attempt which took a little touch off Vorm on the way through only to see Steven Caulker make a courageous goal-line clearance as he crashed into the upright.
Scott Sinclair was inches way from leveling for the visitors when he put his long range free-kick onto the crossbar in the 54th minute before Arsenal captain Robin van Persie hit the woodwork down the other end with a brilliant piece of play which ended with his right-footed attempt skimming the upright.
And perhaps the other 'moment' apart from Vorm's howler came in injury-time when Graham missed from six yards out as he struck on the turn but he put it over the bar when he should have leveled as Szczesny had come off his line and was stranded in no-man's land.
Thankfully for Arsene Wenger's men, the killer blow was not landed and the North Londoners eased the pressure off themselves to move to 11th as Swansea went to 17th after a fourth top flight match without a goal.
TRIBAL ASKS: Has this result made life easier for Arsenal or are there still plenty of shortcomings in their game?
Match facts:Arsenal's third win in 15 PL matches since Carling Cup loss last season.
First meeting between the clubs since 1983.
Mikel Arteta and Per Mertesacker made Arsenal debuts as starters and Yossi Benayoun did likewise from the bench. 32-year old Mark Gower played his first PL game for Swansea as did ex-Villa, West Brom defender Luke Moore.