The Anglo-Nigerian, paired in attack with Ghana international Jordan Ayew, contributed the assist for the Swans's opener as they got to a perfect start.
In the 22nd minute, and against the run of play, the striker pounced on a loose ball before splitting the Gunners’ defence with a pass for Samuel Clucas to finish past Petr Cech.
Paul Clement’s men went into the break with the lead but were brought level by a Saed Kolasinac strike in the 51st minute.
Immediately, Abraham scored at the other end to put the visitors back in front but it was ruled out for offside and, thus, would have to wait for his fifth league strike.
Aaron Ramsey’s strike in the 58th minute broke the heart of the travelling supporters.
Ayew was on parade for 81 minutes while the youngster played for the entire duration of the tie as the Liberty Stadium outfit suffered their fourth loss in the league of the season.
Nigeria’s Alex Iwobi watched from the sidelines as Arsene Wenger’s side secured their sixth win in the English topflight.