The Gunners recorded a fifth straight league win after second-half goals from German teenager Serge Gnabry and in-form Wales midfielder Aaron Ramsey proved enough to see off the home side.
There was, though, a nervy finale at the Liberty Stadium after a well-worked goal from Ben Davies, but Arsenal marked Arsene Wenger's 17th anniversary with a hard-fought victory.
Manchester City went down 3-2 at Aston Villa after a second-half rally by Paul Lambert's men. Yaya Toure slotted home following a corner just before half-time to put City ahead.
Villa levelled through Karim El Ahmadi on 51 minutes. Replays suggested the Morocco midfielder was offside. City were quick to respond and led again when Edin Dzeko bundled in a corner five minutes later.
But Villa were level when Leandro Bacuna clipped in a 20-yard free-kick in the 73rd minute before going ahead seconds later with another quick goal, this time from Andreas Weimann.
John Terry's header earned Chelsea their draw at Tottenham.
Tottenham dominated the first half and took the lead through Gylfi Sigurdsson, but Terry's goal set up what looked to be a thrilling finish. It was overshadowed when, on 81 minutes, referee Mike Dean showed Fernando Torres a second yellow card for elbowing Jan Vertonghen.
Cardiff heaped more pressure on Fulham manager Martin Jol as a stoppage-time strike from Jordon Mutch earned the Welshmen a 2-1 win at Craven Cottage.
Hull beat West Ham 1-0 at the KC Stadium, with an early penalty from Robbie Brady.
Southampton maintained their promising start with a 2-0 victory over struggling Crystal Palace at St Mary's Stadium.