Ruben Amorim made six changes to his line up for the match with Zirkzee, Marcus Rashford, Kobbie Mainoo, Casemiro, Amad Diallo and Diogo Dalot all starting at Old Trafford.
United were fortunate to be up against the joint-lowest scoring side in the Premier League as Everton wasted a number of good openings early on as Beto fired wide from a tight angle while at the other end Amad scuffed his effort after a fine pass from Zirkzee.
In a first-half lacking in quality, United finally opened the deadlock ten minutes before the break, when Rashford's first-time effort from a corner was turned into his own net by United transfer target Jarrad Branthwaite. United were buoyed by the goal and soon had a second. Amad dispossessed Branthwaite in his own half before passing the ball to Bruno Fernandes, who squared for Zirkzee to fire in only his second goal since signing.
Early goals had been a feature of United's opening two matches under Amorim and they had another against Everton, when Rashford netted just 19 seconds into the second-half after some excellent build-up play between Zirkzee and Amad.
It didn't take long for those worries to be put on hold though. United soon had a fourth when Amad worked hard to win the ball back on the halfway line and eventually set-up Zirkzee for his second goal of the game to put the contest firmly to bed and earn Amorim his first league win as head coach.
Here is how we rated the United players in the win over Everton:
A quiet game for him in the United goal. He claimed crosses well and operated well as a sweeper keeper when required but there wasn't much to do.
1. Andre Onana - 6
A quiet game for him in the United goal. He claimed crosses well and operated well as a sweeper keeper when required but there wasn't much to do. | Manchester United via Getty Images
Another match in which he did all the simple things well. Mazraoui has to start on recent form and he is making a centre-back role his own.
2. Noussair Mazraoui - 6
Another match in which he did all the simple things well. Mazraoui has to start on recent form and he is making a centre-back role his own. | Manchester United via Getty Images
His mobility was an issue against the physical Beto. United were fortunate not to be punished for their poor defending in the first-half.
3. Matthijs de Ligt - 5
His mobility was an issue against the physical Beto. United were fortunate not to be punished for their poor defending in the first-half. | Getty Images Photo: Getty Images
A solid performance in central defence. He started attacks as well as he ended them, and brought balance to the backline but was needlessly booked for a silly foul on Beto.
4. Lisandro Martinez - 5
A solid performance in central defence. He started attacks as well as he ended them, and brought balance to the backline but was needlessly booked for a silly foul on Beto. | Manchester United via Getty Images