When the two sides met in November’s league phase encounter, Alkmaar got off to a breathless start and took the lead inside two minutes.
And the Dutch side once more started off on the front food, netting a stunning opener on 12 minutes when Sven Mijnans produced an inch-perfect freekick from distance.
The home side continued to dominate the early stages as Galatasaray were rooted firmly on the back foot, and Ernest Poku was played in on goal, but after rounding the goalkeeper his shot was superbly blocked.
That miss looked as though it would prove costly, as the Turkish outfit went up the other end and netted the equaliser.
Alvaro Morata collected the ball over the top of the Alkmaar defence, but his reverse pass was cleared to the edge of the box, where Roland Sallai unleashed an unstoppable first-time strike into the top corner.
Abdulkerim Bardakci had a shot saved from a tight angle too, before the Cheese Heads restored their lead from the penalty spot before the break.
After attempting to clear the ball, Baris Alper Yilmaz brought Seiya Maikuma down in the box, and Troy Parrott stepped up to slot his fourth UEL goal of the campaign.
Okan Buruk would have wanted an improvement from the Lions in the second half, but his team talk was dashed within six minutes of the restart, as his side were reduced to 10 men after Kaan Ayhan was sent off for a second bookable offence.
Things went from bad to worse for the Turks as Alkmaar doubled their advantage minutes later.
A spell of possession culminated with Jordy Clasie collecting the ball in the box and sliding it past Fernando Muslera with a simple finish.
Two goals to the good and with a man advantage, Alkmaar wrapped up the contest for the evening on 66 minutes after David Moller Wolfe followed up on the rebound from a saved Mijnans shot.
The Dutch side coasted through the remainder of the half, maintaining their advantage going into next week’s second-leg tie in Istanbul, where Galatasaray are unbeaten in 15 home games across all competitions.
Flashscore Man of the Match: Sven Mijnans (AZ Alkmaar)