The Dutch giants will also endeavour to avenge last month's defeat to the Seagulls, who saw off the hosts 2-0 at the Amex to claim a maiden continental win at the third attempt.
Match preview
If one will pardon the pun, John van 't Schip has certainly steadied the ship since wandering into the Ajax dumpster fire, taking over a team who had suffered four successive defeats and lost 10 games on the bounce during their sleepwalk to the Eredivisie basement.
As Halloween passed, though, so did Ajax's horror show, and the hosts enter Thursday's game having clinched back-to-back Eredivisie wins for the first time this season, firstly putting two unanswered goals past Volendam before comfortably dispatching Heerenveen.
Luuk Browers's late first-half strike did set up a nail-biting second half after Steven Bergwijn and Brian Brobbey propelled Ajax into a two-goal lead, but an inspired substitution from Van 't Schip saw ex-Middlesbrough man Chuba Akpom net a brace in the final 10 minutes to seal a comprehensive 4-1 rout.
Shooting up to 11th in the Eredivisie standings on account of their mini-revival, Ajax have also conceded just once in their last 180 minutes of football after shipping 24 goals in the eight matches before Van 't Schip's arrival, and their Europa League last 16 fate remains in their own hands.
A two-point haul currently sees Ajax languish at the bottom of the section, but the Sons of the Gods have the chance to move level on points with section leaders Marseille should they avoid starting a continental campaign without a win after four games for the first time since the 2015-16 Europa League.
Brighton's Europa League openers with AEK Athens and Marseille saw Roberto De Zerbi's vivacious attacking forces score two goals on each occasion, only to be let down by rearguard indiscipline as they walked away from those meetings with just one point to their name.
However, the Seagulls had little trouble quelling the Ajax offence last time out and continued their multiple-goal sequence through Joao Pedro and Ansu Fati to make it third time lucky in Group B, cementing their place in Brighton history with their first-ever win in European competition.
The third-placed visitors continue to play catch-up in the section, though, as they are one point adrift of Marseille and below AEK Athens on head-to-head points, but should their two adversaries play out a draw in Thursday's top-of-the-table clash, first place will be theirs if they can do the double over Ajax.
Brighton's domestic exploits have left a lot to be desired, though, as De Zerbi's team have failed to win any of their last five Premier League matches and needed an Ashley Young own goal to rescue a point in a 1-1 draw with Everton at the weekend, where profligacy denied them a much-needed maximum.
Young's unfortunate contribution did at least stretch Brighton's scoring run in all tournaments to seven games, but Dutch sides have often had their English counterparts' number in that department; Premier League teams have failed to make the net bulge in each of their last three Europa League visits to Eredivisie soil.
Ajax Europa League form:
W
L
D
D
L
Ajax form (all competitions):
L
L
L
L
W
W
Brighton & Hove Albion Europa League form:
L
D
W
Brighton & Hove Albion form (all competitions):
D
D
L
W
D
D
Advert - content below:
Team News
Ajax attacker Bergwijn was a little worse for wear after he was taken off at the Amex two weeks ago, but the ex-Tottenham Hotspur man has shaken off that affliction and should start on the left-hand side of a B-themed Ajax frontline alongside Brobbey and Steven Berghuis, unless Akpom's brace puts him in Van 't Schip's thinking.
A quartet of Amsterdam-based players are still struggling with injuries, though, as Geronimo Rulli (shoulder), Sivert Mannsverk (leg), Jay Gorter and Amourricho van Axel Dongen (both unspecified) are set to sit out the visit of the Seagulls.
Van 't Schip should see little need to disrupt the harmony of a winning team, but the experienced Borna Sosa is a candidate to displace academy product Arjany Martha at left-back.
As far as Brighton are concerned, De Zerbi has a similar handful of fitness concerns to factor in for Thursday's game, including knee victims Solly March, Julio Enciso and Jakub Moder, although the latter is at least beginning to build up some match fitness with the Under-21s.
Danny Welbeck is also facing an extended period on the sidelines with the injury he sustained towards the end of October, and De Zerbi is not optimistic about Pervis Estupinan's chances of returning from a thigh injury before the November international break.
The Seagulls boss has not been afraid to rotate his resources to cope with the demands of Premier League and Europa League football, and anticipated changes ought to lead to Fati and Pedro both earning recalls to the frontline as they aim to haunt the Ajax rearguard again.
Ajax possible starting lineup:
Ramaj; Rensch, Sutalo, Hato, Sosa; Taylor, Tahirovic, Van den Boomen; Berghuis, Brobbey, Bergwijn
Brighton & Hove Albion possible starting lineup:
Steele; Veltman, Van Hecke, Dunk, Milner; Fati, Gross, Gilmour, Mitoma; Pedro, Ferguson
We say: Ajax 1-1 Brighton & Hove Albion
Since locking horns on England's South Coast two weeks ago, Ajax have been on an upward trajectory under their new manager, while Brighton have hit a Premier League plateau amid their raft of injuries.