Interim head coach Van Nistelrooy will hand over the reins to Ruben Amorim this week and wait to find out if he still has a job.
He will leave behind a team unbeaten in his four games, and with some momentum and goals behind them at last.
Bruno Fernandes opened the scoring inside 20 minutes with a delightful finish, to celebrate his 250th United appearance in style.
An own-goal from Victor Kristiansen doubled their advantage, before substitute Alejandro Garnacho sealed Leicester's fifth league defeat of the season with a stunning strike.
Van Nistelrooy had dropped Garnacho in favour of Amad Diallo, who scored twice in the win against PAOK in the Europa League last Thursday.
Centre-back pair Lisandro Martinez and Matthijs de Ligt were also recalled.
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