Eddie Nketiah had given Arsenal the lead with a curling finish after Reiss Nelson’s run from the halfway line.
Danny Welbeck, who played for the Gunners in the 2018 final, made it 1-1 with a penalty after he had been fouled by debutant home goalkeeper Karl Hein.
Kaoru Mitoma put Brighton ahead after a neat passing move and Tariq Lamptey added a third with a low strike.
The loss in this third-round tie was only the third time in 20 matches in all competitions that Arsenal had been beaten this season.
Mikel Arteta made 10 changes from the 1-0 win at Chelsea and the Gunners looked on course for the last 16 when they took the lead through Nketiah’s excellent 20th-minute strike.
However, their lead only lasted seven minutes.
Hein, a 20-year-old Estonia international goalkeeper who had a loan spell at Reading last season, was making his first senior appearance for the Gunners but brought down Welbeck, who then converted the spot kick.
Arsenal almost retook the lead when Nketiah fired a shot against the post from outside the penalty area with Albert Sambi Lokonga also shooting just wide.
Those misses proved costly as Mitoma got his second goal for Brighton in five days after also scoring in the 3-2 win at Wolves on Saturday, before Lamptey added a third.
Brighton’s best performance in the EFL Cup came in 1978-79 when they reached the quarter-finals, but this is now the third successive season where they have reached the last 16.
The draw for the next round will take place on Thursday night, following the match between Manchester United and Aston Villa at Old Trafford.