Newcastle scored four first-half goals for the first time in seven years to leave themselves in the driving seat for a place in the quarter-finals.
Obafemi Martins scored twice to take his tally for the season to 16 and was joined on the scoresheet by Kieron Dyer and a Gretar Steinsson own goal.
Veteran former Rangers marksman Shota Arveladze pulled back an opening half goal and Danny Koevermans got the only goal after the break, after Shay Given had saved a Moussa Dembele penalty.
Newcastle got off to a dream start in what was a breathtaking first half.
The fit-again Damien Duff produced an exquisite flick to release Dyer on the left and his low drive was turned into his own goal by Steinsson under pressure from Martins.
There then followed two goals in 60 seconds after 22 minutes once again courtesy of an audacious flick. Nobby Solano and Nicky Butt combined before Sibierski flicked Dyer in the clear and his finish was devastating.
Shell-shocked Alkmaar were still reeling when they went 3-0 down when Martins was put clear, cut inside to beat two players and shot right-footed across Boy Waterman
It was a case of deja vu for Alkmaar boss Louis Van Gaal, who will have recalled in the Champions League in 1997 when he was in charge of Barcelona, they trailed 3-0 to a Faustino Asprilla hat-trick.
The Catalans came back to lose that game 3-2 before winning 1-0 at the Camp Nou to win on away goals.
And Van Gaal must have hoped for something of the same when 35-year-old former Rangers striker Arveladze scored with a stunning diving header which went in off the underside of the bar.
Clearly lifted, Alkmaar forced two excellent saves out of Given, United's most experienced campaigner in their European history, who was making his 61st appearance - nobody else has topped 50.
But the Dutch side were stunned after 37 minutes following a foul on Martins. From the free-kick Scott Parker released Solano on the right to cut inside and pull back the ball for Martins who crashed another right-footed shot beyond Waterman to make it 4-1.
It was always going to be hard for the second half to live up to the opening 45 minutes and United clearly fell off the pace.
And they paid the penalty, literally, when substitute Dembele drove the ball against Steven Taylor's hand and the referee pointed straight at the spot.
Dembele with three UEFA goals this season shot to Given's left and the keeper parried the ball and Parker was first to the ball but slid it straight to the prolific Koevermans who drilled into the net for his third European goal of the campaign.
United's best chance then fell for Martins who broke clear for his best chance of the night, but was kept out by Waterman as he searched to become only the fifth Newcastle player to score a European hat-trick.