Neal Maupay’s header condemned interim head coach Ljungberg to a 2-1 defeat in his first home game in charge.
The Gunners have now gone nine matches without a win, their worst run in over 42 years, with Ljungberg unable to oversee an immediate upturn in fortunes following Unai Emery’s sacking last week.
“It’s tough, they looked low on confidence in the first half,” said Ljungberg. “We need to dig out a win to get some confidence. It’s obvious the nerves in the crowd affect the players.
“They are human beings, they want to do well and they feel pressure. But we need a win and we showed in the second half we can get one.”
Brighton were dominant against a limp home side and took a deserved lead from a corner, Adam Webster sweeping the ball home from Dan Burn’s knock-down and Aaron Connolly’s touch into his path.
Arsenal should have drawn level before half-time after Pierre-Emerick Aubameyang stood up an inviting cross, but Joe Willock could only head it at Mat Ryan, who had got across well to save with his feet.
Ljungberg threw on record signing Nicolas Pepe at the break and Arsenal immediately looked brighter.
It took them four minutes to equalise, Alexandre Lacazette’s flicked header from Mesut Ozil’s corner looping up and flying in off the far post as Sead Kolasinac challenged Ryan.
David Luiz had the ball in the net after an hour but he was clearly offside when he met Ozil’s free-kick and VAR chalked off the goal.
Instead Brighton secured a notable win when Aaron Mooy was given too much space down the left to swing in a cross and Maupay got ahead of Luiz to glance a header home.
Arsenal almost snatched a point but Ryan kept out a late header from substitute Gabriel Martinelli.
It meant Seagulls boss Graham Potter was able to repeat his Europa League triumph over the same opposition at the Emirates with Swedish minnows Ostersunds in February last year.
“Thursday nights at Arsenal are great!” smiled Potter. “Hopefully the Premier League will arrange more games on a Thursday.”
Brighton’s second away win of the season – and a first ever at Arsenal – lifted them above Aston Villa, West Ham and Bournemouth into 13th.
Potter added: “We showed great quality and great courage, so overall I’m delighted with the players. It’s fantastic to get three points and play like we did.
“Given the quality up front they have everything can change, but credit to the players, they managed the situation well, and there was a bit of quality from us as well.
“We’ve had a tough batch of games so it’s nice to come away from home, win, and play well. It gives us a bit more confidence on the path to going somewhere.”