The Seagulls, who are having a great time in their maiden season at this level of play, drew at Marseille after losing their opening Group B match at home to AEK Athens.
However, they had a historic night at Amex Stadium against the seasoned European team Ajax, as goals from Joao Pedro and Ansu Fati sealed the win.
“We have got the first victory in Europe for Brighton,” manager Roberto de Zerbi told TNT Sports.
“It is a great day for our fans, our club, our owner and we are very proud to give them this day.”
Just before the interval, Pedro scored his fourth goal of the Europa League after Ajax goalkeeper Diant Ramaj parried a well-struck shot by Kaoru Mitoma.
After the break, it was even better as Brighton scored a second goal with a brilliant pass from Simon Adingra to Fati, who took two touches inside the box before finishing the shot into the corner of the net.
As he struck the post for Ajax, Steven Berghuis cautioned Brighton not to let their guard down, but the visitors had few other opportunities as the Seagulls easily won.