Neal Maupay headed in a deserved winner for the Seagulls 10 minutes from time after Alexandre Lacazette had cancelled out Adam Webster's opener for Brighton.
Defeat leaves Arsenal in 10th and 10 points adrift of fourth-placed Chelsea in the hunt for Champions League qualification next season.
On this evidence there is little chance of Ljungberg landing the job on a permanent basis as another sparse crowd at the Emirates greeted the final whistle with a chorus of boos.
After a 2-2 draw at Norwich on Sunday in the first match since Unai Emery was sacked, there was again no sign of a new manager bounce for Ljungberg's home bow. Brighton dominated the first 45 minutes and could have gone in at the break more than one goal to the good.
Aaron Connolly should have turned Maupay's shot across goal in at the far post before Bernd Leno had to show his reflexes to deny Maupay and Davy Propper with shots from outside the box.
The opener seemed only a matter of time for the visitors and arrived nine minutes before half-time when Arsenal failed to clear a corner and Webster fired home the loose ball from close range.
Going behind woke Arsenal. They could easily have levelled moments later when Joe Willock headed straight at Mat Ryan from Pierre-Emerick Aubameyang's cross.
Willock was sacrificed at the interval as Ljungberg introduced club record signing Nicolas Pepe, who had started on the bench for the fifth straight league game under two different managers.
Ljungberg's half-time tinkering did the trick as the hosts came out a different side in the second half.
Lacazette's looping header brought Arsenal level just five minutes into the second period before Aubameyang was inches away from connecting with crosses from Hector Bellerin and Sead Kolasinac.
Brighton still posed a threat themselves and fired a warning shot when Maupay failed to beat Leno from point-blank range.
David Luiz thought he had put Arsenal in front as he turned home from Mesut Ozil's free-kick only for the Brazilian to rightly be ruled offside after a VAR review.
Brighton made the most of that reprieve to win on the road in the Premier League for the first time since the opening weekend of the season as Mooy's cross picked out Maupay to head into the far corner.
Elsehwere, Newcastle taught Sheffield United a lesson in taking their chances as the Magpies won 2-0 at Bramall Lane despite enjoying just 27 percent possession.
Allan Saint-Maximin headed the visitors in front with his first goal for the club and Jonjo Shelvey secured the three points when he played on as the Blades defence stopped at the sight of the offside flag going up against Andy Carroll.
A VAR review showed Carroll was onside as he flicked the ball into Shelvey's path.