Ajax have been facing troubles this season after a ponderous summer transfer window left the squad lacking quality and experience.
Manager Maurice Steijns has been sacked, leaving them in the Eredivisie relegation zone.
Interim coach Hedwiges Maduro set the team up to be compact against the Premier League side, handing control to the Seagulls.
Joao Pedro opened the scoring just before the half-time break, pouncing to score as Diant Ramaj spilt a hot shot from Kaoru Mitoma.
The former Eintracht Frankfurt goalkeeper had made two good saves to keep his side in the tie but could do nothing as the Brazilian slotted home from close range.
Roberto De Zerbi’s side took the 1-0 lead into the dressing room at half-time.
They doubled their lead soon after the break. Ansu Fati collected a lovely pass from Simon Adingra before finishing with aplomb.
The Barcelona loanee is adapting to life in his new surroundings, bagging three goals for the Seagulls in nine outings across all competitions.
Steven Berghuis hit the Brighton post as Ajax sought redemption after a listless showing, but it was not to be.
Brighton took the three points and moved above Ajax in Group B.
The Seagulls still have three matchdays to climb into one of the top two spots in the group, with Marseille and AEK Athens currently ahead of them.
Ajax will hope they can turn their abysmal season around as things continue to veer further south for the record-time Dutch champions.
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