The loss leaves Arsenal in sixth place and 13 points behind Tottenham in fourth, while Brighton climb into the top half of the table.
Arsenal's French manager Arsene Wenger gestures on the touchline during the English Premier League football match between Arsenal and Manchester City at the Emirates Stadium in London on March 1, 2018.
Europa League glory remains up for grabs to the Gunners, but they are set to face Italian giants AC Milan at the last-16 stage of that competition and the contrast in form between two continental rivals heading into that contest could not be more marked.
Brighton's first win over Arsenal since 1982 lifted the team into 10th place, seven points above the relegation zone in its first season in the Premier League.
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It is the earliest an Arsenal side have been mathematically eliminated from the title race in the history of playing in a 38-game season and under Arsene Wenger. "It is not the first time I have lost so many games in row".
Shortlisted replacements such as Joachim Low and Leonardo Jardim will need huge investments to turn around the fortunes of the team.
It was almost 2-0 minutes later as Gross sent Cech sprawling to save at his near post, and Dunk headed over after 18 minutes from another corner by Gross.
Speaking at the post-match press conference, Wenger said: "I must tell you, honestly, at the moment my future is not my main worry".
Arsenal's lacklustre display was summed up by the way Alex Iwobi was easily dispossessed inside his own half by Anthony Knockaert who was denied only by another good save from Cech. His cross was met by Murray in the six-yard box and the ball squeezed beneath the body of Cech to prompt some "Wenger out" chants in the away end.
Arsenal would go on to dominate possession and had a chance to snatch a draw at the end through Aubameyang, who failed to get the better of home keeper Mathew Ryan.