The 27-year-old played in his favoured number ten role behind Olivier Giroud but was unable to provide his 19th assist of the season.
Arsenal looked set to record a comfortable home victory when Joel Campbell found the back of the net after just 15 minutes.
However, Wayne Routledge levelled the scored 17 minutes later while Swansea captain Ashley Williams scored the winner midway though the second half.
Arsenal 1 – 2 Swansea:
Kick-Off: 19:45 (GMT)
Stadium: Emirates Stadium
confirmed lineup: Cech, Bellerin, Gabriel, Koscielny, Monreal, Coquelin, Ramsey, Campbell, Ozil, Sanchez, Giroud
Subs: Ospina, Chambers, Gibbs, Elneny, Flamini, Walcott, Welbeck
Swansea Lineup: Fabianski, Naughton, Amat, Williams (c), Kingsley, Cork, Fer, Ki Sung-Yueng, Routledge, Ayew, Gomis
Subs: Nordfeldt, Rangel, Fernandez, Fulton, Barrow, Sigurdsson, Paloschi
Goals: .15 Campbell (Arsenal), .32 Routledge, .74 Williams (Swansea City)