A slow first half saw the Red Devils burst into life after the interval, as United scored four in 11 minutes.
Ashley Young fired home from a tight angle after 53 minutes, and Mason Greenwood found the bottom corner five minutes later.
Jordy Clasie fouled Greenwood in the box on 62 minutes, allowing Juan Mata to slot home from the penalty spot.
Greenwood completed his brace two minutes later, and United extinguished Dutch hopes during a frenzied spell of attacking football.
It was a tale of two halves in Manchester, as United turned on the style with their rotated side.
Alkmaar, currently second in the Eredivisie, held their own before the half-time whistle, but they were shell-shocked early in the second half.
Greenwood showed why he's so highly rated at United, and the 18-year-old produced an impressive all-round striking display.
Andreas Pereira danced his way from the corner flag to the box before passing to Nemanja Matic, and the Serb slid the ball into Mata. The Spaniard's cross was met by Young at the far post, who smashed the ball home.
The opener set off a chain of events that destroyed Alkmaar's game, and it was Greenwood who took the plaudits.
United raided in numbers, and the forward produced two convincing strikes to beat goalkeeper Marco Bizot.
Greenwood was involved in all three goals after Young's effort, firing from distance with a clean strike that beat Bizot with pace.
The England U21 player was then hacked down by Clasie as he skipped into the penalty area, and Mata made no mistake with a calm penalty.
The Bradford-born prodigy wasn't finished. Greenwood drove into the box in the right channel, and once again, the power of his effort was too much for Bizot.
United continued to dominate the flow of traffic, with Ole Gunnar Solskjaer appearing relaxed and satisfied in the dugout.
Both teams are back in domestic action on Sunday. United host Everton in the Premier League, while Alkmaar welcome Ajax, who drop down into the Europa after failing to advance in the Champions League, in the Eredivisie.