Goals from Leandro Trossard and Enock Mwepu gave Graham Potter's side all three points for the first time in eight Premier League games.
Martin Odegaard gave his side hope when his effort from 30 yards was deflected by Danny Welbeck, which looped the ball over goalkeeper Robert Sanchez.
But it was not enough for the hosts, who will be left fuming over VAR after having an equaliser on the stroke of half-time ruled out after a lengthy delay.
After a damaging result on Monday night against Crystal Palace, the Gunners had to win this game to get their top-four hopes back on track.
Prior to kick-off, a point would have been enough for Arsenal to go back in the final spot above fierce rivals Tottenham, even for a few hours.
But from the first minute, Mikel Arteta's side never looked like they brushed off the defeat at Selhurst Park and if anyone looked like taking a lead, it was the Seagulls.
Chances were few and far between in the first 25 minutes, but the game finally came to life on the half-hour mark.
With first choice left-back Kieran Tiernay out for the rest of the season, Arteta opted to deploy defensive midfielder Granit Xhaka in that position.
Whilst Xhaka has certain abilities, pace is not one of them, and it was on display for the opener.
A clearance from Lewis Dunk found Mwepu, and for some reason the Switzerland captain was not in line with the rest of his back four.
With a gaping hole in his position, the 24-year-old Zambian exploited the space and after proceeding into the penalty area, he cut the ball back to Trossard who unleashed an unstoppable strike into the top right corner past Aaron Ramsdale.
It was a fantastic goal from the visitors, but one that could have been avoidable had Xhaka been in the right position.
Finding themselves 1-0 down again, Arsenal's character was tested, and they didn't look like showing much of that for the remainder of the first half.
However, on the stroke of half-time, it looked like the hosts got out of jail.
An in-swinging corner from Bukayo Saka found Gabriel at the far post, he knocked it across goal and, a few yards out, Gabriel Martinelli had the simple task of heading the ball into an empty net.
It was a huge relief for everyone in the ground other than the Brighton fans, but just as the hosts thought they got back on terms, VAR intervened.
After a lengthy check from the officials, the Brazilian was adjudged to be offside.
Whilst the correct decision was made, it was another frustrating wait for fans as they were made to wait.
And speaking on talkSPORT, former West Ham centre-back Alvin Martin was extremely critical for how long it took for a call to be made.
"I'm not a fan i don't think any of us are, it's ridiculous really,"
"I think it's taken a massive part of the game away, VAR, he has got it right, but at the cost of what to the game?
"Not just this game, but every game."
Much of the second half was a replica of the first, and to sum up Arsenal's woes, Saka was correctly booked for simulation.
The hosts' misery was then compounded when Brighton doubled their lead just after the hour mark with an incredible team goal.
On the left channel, Marc Cucurella played the ball into Moises Caicedo who gave it Trossard, his wonderful flick returned the ball to the Ecuadorian and he cut the ball back to Mwepu.
20 yards out, the Zambian produced a wonderful side-footed effort into the bottom left.
Arsenal tried to get back into it, and could have even snatched a point at the end after Odegaard's strike made it 2-1 just before the clock hit 90 minutes.
But they couldn't test Sanchez again as Arsenal's top four hopes suffer a major dent.