The visitors mirrored their 2-0 victory at the Amex on October 26 with this victory in Amsterdam thanks to goals from Ansu Fati and Simon Adingra.
Overall it was a superb performance from Brighton who were in desperate need of a win to boost morale as the side are without a victory in the Premier League since late September.
The Seagulls are currently top of their Europa League with seven points while Ajax, who have had a disappointing start to their league season winning just three from their first 10 games, remain bottom with two points.
1. Bart Verbruggen: 8
The Dutchman made some clean saves and barely put a foot wrong. Photo: (Photo by Mike Stobe/Getty Images for Premier League)
2. James Milner: N/A
The adaptable veteran came off after six minutes with an injury Photo: (Photo by Jess Hornby/Getty Images)
3. Jan Paul van Hecke: 9
The Dutchman looked comfortable on the ball, even when he was put in awkward situations. He showed glimpses of a superb player who could be vital in the near future. Photo: (Photo by Mike Hewitt/Getty Images)
4. Lewis Dunk: 7
The captain looked solid at the back but was unfortunately substituted at half-time after picking up what looked to be a groin injury. Photo: (Photo by Mike Hewitt/Getty Images)