The Gunners will now kick off the New Year in 13th place after Alexandre Lacazette secured a vital three points.
Despite showing signs of moving in the right direction in recent weeks, the Gunners were second best in the first half, as Brighton created the better chances.
Alireza Jahanbakhsh’s low drive was the best Graham Potter’s team could muster in the first 45 with Bernd Leno equal to his effort.
Arteta’s side did slowly begin to turn the tide after the break as Pierre-Emerick Aubameyang tested Robert Sanchez and Gabriel Martinelli fired over.
And as Arsenal found themselves in the ascendency late on, Lacazette grabbed his chance to put them in front.
Bukayo Saka’s driving run had the Brighton defence on the back foot and Lacazette collected his square ball to fire home.
Neither side were able to create a grandstand finish on the south coast as Arsenal grabbed back to back wins for the first time since the opening day.
Full Time at the Amex Stadium it’s Brighton 0 Arsenal 1