At Anfield, Liverpool eased to a comfortable 4-0 win over LASK to secure top spot in Group E and a place in the last 16.
Meanwhile, Tomas Soucek's late winner earned the Hammers all three points against Backa Topola in Serbia.
How Brighton's match unfolded
Roberto De Zerbi handed Jack Hinshelwood a Europa League debut, while Kaoru Mitoma returned after recovering from injury. Joao Pedro was also recalled to the starting XI following his double off the bench in last weekend's 3-2 win at Nottingham Forest, replacing the injured Ansu Fati.
Brighton struggled to create chances in the first half, with AEK coming closest to opening the scoring when Steven Zuber's shot was deflected on to a post by a sliding Lewis Dunk.
The Seagulls opened the scoring on 51 minutes from the penalty spot after Joao Pedro was fouled by Damian Szymanski.
Brighton's Brazilian calmly sent Cican Stankovic the wrong way for his eighth goal of the season.
AEK were reduced to 10 men in the 65th minute after midfielder Mijat Gacinovic fouled Joel Veltman and was shown a second yellow card.
Domagoj Vida missed a great chance to equalise for the home side, but he headed wide from 12 yards out as Brighton held on for a historic win.
The win means Brighton will be playing in the next phase of the competition, although they need to beat Marseille in their final Group B fixture at Amex Stadium on 14 December to secure top spot and avoid featuring in the playoff round.
De Zerbi's side are back in Premier League action on Sunday when they travel to Chelsea.
Group B standings
How Liverpool's match unfolded
Liverpool's front three combined brilliantly for the second goal three minutes later, Diaz finding Salah, who squared for Cody Gakpo to tap in at the far post.
Salah made it 3-0 on 51 minutes, scoring from the penalty spot after Gakpo had been fouled by LASK goalkeeper Tobias Lawal.
Gakpo added a fourth in the second minute of added time, latching on to a superb pass from substitute Trent Alexander-Arnold to put the icing on Liverpool's 10th consecutive home win.
The Reds, who travel to Belgian side USG in their final group match, now avoid February's playoff round.
Up next for Klopp's men in the Premier League is a home encounter with Fulham on Sunday.
Group E standings
How West Ham's match unfolded
The Hammers lacked cohesion for much of the contest, only managing a single shot on target before Soucek provided the game's decisive moment in the 89th minute.
Latching on to Maxwel Cornet's brilliant cross, the Czech volleyed in from close range to make it two late winners inside a week, after doing so against Burnley.
Soucek now has five goals in his last five games for club and country.
It leaves Moyes' side top of Group A, only needing a point against Freiburg in the final round of group matches to earn top spot, and avoid a playoff in February against a side finishing third in their UEFA Champions League group.
Up next for West Ham in the Premier League is Sunday's home encounter with Crystal Palace as they look to extend their winning run in all competitions to five matches.
Group A standings
How Aston Villa's match unfolded
Diaby opened the scoring after only four minutes, cutting in from the right before curling a shot past Legia goalkeeper Kacper Tobiasz.
But Villa's lead only lasted 16 minutes, with Legia equalising through Ernest Muci.
Emery's men restored their advantage on 58 minutes, with Moreno marking his return with his first goal for the club, volleying in from Douglas Luiz's free-kick.
That goal proved enough for Villa to progress from the group, but they will need a point in their final match at Zrinjski in two weeks to bypass the playoff round and go straight into the last 16.
They'll hope to build on back-to-back wins in all competitions with a third victory in seven days when they visit AFC Bournemouth on Sunday.
Group E standings