Nacho Monreal opened the scoring in the first half before Alex Iwobi secured all three points after the break.
Arsenal climb to fifth in the Premier League table while Brighton remain 14th.
But what did we learn from the game?
The contract rebel returned to the starting XI after being rested for the Europa League win against BATE Borisov.
He was at the heart of their attacking player all afternoon and capped off a decent display with a cheeky back heel for Iwobi’s goal.
Mesut Ozil missed the game due to injury but his absence was not felt on the pitch.
Arsenal should have enough to beat Brighton without Ozil but Sanchez and Iwobi linked up well behind Alexandre Lacazette.
Aaron Ramsey and Granit Xhaka dominated the midfield from the first whistle and are impressing as a pair.
Stiffer tests lie ahead but these two provide a solid base for Arsenal’s attacking stars to do their stuff.
Sead Kolasinac on a free transfer is, arguably, one of the most impressive pieces of business by any club in the summer transfer window.
He was tactically disciplined and bombed forward when the result was guaranteed.
Brighton’s best hope of staying in the Premier League is to keep winning their home games.
They are unlikely to pick up many points on the road but can take heart from causing Arsenal problems on occasions.
