Van Gaal’s side equalled their biggest Premier League win of the season thanks to goals from Jesse Lingard, Anthony Martial and Wayne Rooney.
And the timing couldn’t have been better as United delivered a strong performance 24 hours after the high-profile appointment of Pep Guardiola as manager of their bitter rivals Manchester City.
Guardiola’s impending arrival in the close-season as the replacement for Manuel Pellegrini is designed to make City the dominant force not only in Manchester but also in Europe.
United look to be in danger of falling behind their neighbours as they struggle to even qualify for next season’s Champions League, while question marks persist over their managerial position.
Van Gaal was booed by United’s supporters after their last home game – a 1-0 defeat to Southampton.
But the Dutchman has clung onto his job and this result – allied to a superb attacking performance – keeps them within five points of the top four places and should buy van Gaal a little breathing space.
United had won just two of their previous 10 league games and scored only 11 home goals.
Their total of 27 goals in total at this stage of the season was their lowest since 1989-90 when they finished 13th in the top flight and Mark Hughes finished as top scorer with 15 goals.
Hughes was back on his old stamping ground as Stoke manager, but it was not a happy homecoming as his 100th Premier League match in charge of the Potters ended in a chastening defeat and prolonged Stoke’s winless record at Old Trafford, which stretches back 40 years.
A victory over United on Boxing Day, which threatened to push Van Gaal close to the exit door, gave Stoke the chance to complete the double over United for the first time since 1952-53.
But that never looked likely as United raced into a 2-0 lead inside the first 23 minutes.
– Memories -United showed their intent from the start as they created more chances than they had in most of their home games put together.
And they went ahead in the 13-minute when teenage full-back Cameron Borthwick-Jackson crossed for Lingard to stoop and head in his third goal of the season.
Martial then fired into the side netting and forced Jack Butland into a save before he scored a superb goal to take his total for the season to nine.
United launched a lightning break, bringing back memories of some of their finest football under Alex Ferguson, which ended with Rooney teeing up Martial to curl a superb right-footed shot into the top corner.
Stoke, unable to use record signing Giannelli Imbula after his late arrival on Monday, couldn’t handle Juan Mata, who excelled in a central position and could have had a hat-trick as he saw efforts blocked and headed wide from a Matteo Darmian cross.
Jon Walters did go close for the visitors, whose season is falling apart around them after two cup exits in a week and a third league game without a win, as he volleyed over before the break.
But they had no answer to a classy United performance which included a goal from Rooney after the break.
The United and England captain had an effort disallowed as he barged over Phil Bardsley in the build-up.
But Rooney wouldn’t be denied a seventh goal in as many games as he tapped in a Martial cross following another flowing move with 53 minutes gone.
And as United made a long overdue statement of intent they almost added a fourth when substitute Memphis Depay hit the bar with an angled shot late on.