Arsenal missed their chance to go back to the top of the Premier League after being forced to play with 10 men for much of the game against London rivals Chelsea on Sunday.
Defender Per Mertesacker was sent off in the first 20 minutes for a foul on Diego Costa, who scored the only goal shortly afterwards from a cross by Branislav Ivanovic.
The result preserved the defending champions' unbeaten record under experienced Dutchman Guus Hiddink, who took over as interim manager last month following Jose Mourinho's sacking.
Chelsea moved up to 13th, while Arsenal were left in third place, level on points with Manchester City but three behind leaders Leicester City.
Swansea City's new Italian head coach Francesco Guidolin saw his relegation-threatened team win at Everton for the first time on Sunday to lift them four points above the Premier League's bottom three places.
It was a bad afternoon for highly regarded young Everton defender John Stones, whose poor back-pass led to the 17th minute penalty from which Gylfi Sigurdsson gave Swansea the lead.
The home side soon equalised when Jack Cork touched Gareth Barry's flick into his own net, but a deflection off Stones from Andre Ayew's shot restored the Welsh club's lead before half-time.
They held out amid strong pressure in the second half to move above Norwich City and Bournemouth into 15th place while Everton stayed 12th, four points above them.
