For a second consecutive fixture after the three-month break Mesut Ozil was not involved in the starting XI for Arsenal.
Early in the first half Bukayo Saka had the first clear opportunity to open the scoreline as he shot the ball straight to the goal, but he hit the crossbar.
In the 31st minute, Lacazette had the chance to score a header after a great cross from Saka, but Mathew Ryan made a terrific save.
Just few minutes later, in the 35th minute, Bernd Leno picked up an injury and was forced out of the pitch after a nasty challenge from Neal Maupay.
In the added time of the first half, Aubameyang and Lacazette showed a great class, as the Frenchman made a great backheel pass, but the defender intervened just on time and did not let Auba to finish the ball into the net.
After 67 minutes Nicolas Pepe opened the scoreline after a great curl shot in the far corner. Bukayo Saka was the provider of the assist for the goal.
However, Brighton found the equalizer in the 75th minute, after a set piece as Lewis Dunk reacted very fast and put the ball into the net.
In the added time, an excellent lob by Neal Maupay from Brighton & Hove Albion stole the three points.
Arsenal did not get the much needed three points that could put them closer to any European football next year.