Third-placed Arsenal dominated the early stages and went ahead on 15 minutes when Joel Campbell slid along the ground to half-volley home a pass from Alexis Sanchez on the turn.
Fifth from bottom Swansea equalised against the run of play after 32 minutes as Wayne Routledge slotted in a ball from Jack Cork that had sliced the home defence in two.
The game became stretched in the second half. Arsenal twice came close through Sanchez before goalkeeper Petr Cech missed a cross and Swansea captain Ashley Williams bundled the ball in with 16 minutes to go.
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"I believe we were really unlucky with our finishing and some decisions today," Arsenal manager Arsene Wenger told the BBC. "They had two shots on target and two goals.
"We stopped playing before the first goal because there was a foul on Mesut Ozil. There were hands around his neck and it should have been a free kick for us.
"We need to bounce back very quickly now," added Wenger. "We were unlucky on the night, we were on top and hit the bar a number of times."
(Reporting by Marc Jones; Editing by Tony Jimenez)
