The first half was in keeping with the fact both teams had already qualified but United sprung into life with a flurry of four goals inside 11 second-half minutes.
Teenage forward Greenwood was to the fore after Ashley Young opened the scoring, dispatching a pair of fabulous finishes either side of winning a penalty that Juan Mata converted.
AZ were left to rue a pair of missed chances from Calvin Stengs as United romped clear to be assured of a seeded spot in Monday's draw for the knockout stages.
Andreas Pereira forced AZ goalkeeper Marco Bizot into an early near-post save but the lack of jeopardy in the game was initially reflected by its entertainment levels.
Netherlands forward Stengs dragged unconvincingly wide before the interval and appeared to be caught by surprise when Owen Wijndal's low 47th-minute cross found him in the midst of a disorganised United backline, prodding too close to Sergio Romero.
Anthony Martial fired wastefully over on the half volley after some fine work from Greenwood, and United's 54th-minute opener came from a more unlikely source.
Pereira cleverly twisted out of a tight space by the left corner flag and combined with Mata and Nemanja Matic before the former cut across the six-yard box for the onrushing Young to find the roof of the net from an acute angle.
Greenwood swiftly doubled the lead with an unerring finish from the edge of the box, although AZ were aggrieved that James Garner was not punished for a foul on Fredrik Midtsjo in the build-up.
AZ continued their collapse when Jordy Clasie clumsily brought down Greenwood, and Mata dispatched his penalty beyond Bizot's dive.
There was more to come from the 18-year-old striker, who danced inside Stijn Wuytens and lashed inside the near post in the 64th minute to complete the scoring.