After claiming his first win since taking the helm in Europe on Thursday, Amorim was now seeking his first PL victory as United boss.
The hosts started positively, dominating possession and threatening down both flanks via the new wing-back system implemented at Old Trafford.
Everton took a little while to get going, but following the quarter-hour mark, Sean Dyche’s men began to threaten on the counter, with Beto spearheading the attack. The forward pounced on a loose ball lost by Diogo Dalot but after driving into the box, his shot was skewed wide.
Just as the Toffees looked to be edging proceedings, United went and found the opener on 34 minutes.
A well-worked corner routine saw Bruno Fernandes pick out Marcus Rashford on the edge of the box, and the Englishman’s volley deflected in off Jarrad Branthwaite for his second goal in two PL games.
The wind was in the Red Devils’ sails, and the hosts duly doubled their lead before the break.
Amad Diallo brilliantly won possession high in the Everton half which allowed Fernandes to carry the ball into the box and his square ball was tapped home by Joshua Zirkzee - netting for the first time since the PL opening day.
Dyche would have wanted his side to improve in the second half, but his side’s comeback hopes were undone within 21 seconds of the restart as the hosts netted a third.
Amad broke down the right flank and slipped Rashford in, who made it a brace for the afternoon by slotting through Pickford’s legs.
Clearly shell-shocked, the Everton players struggled to gain a foothold in the contest and eventually conceded a fourth just after the hour mark, with Amad once again running through the heart of the Toffees defence and picking out Zirkzee, who swept home.
Amorim took the opportunity to ring the changes ahead of his side’s upcoming showdown with old rivals Arsenal, taking the sting out of the contest in the process.
Everton failed to recover after conceding so soon after the restart, as United strolled through to a fourth consecutive win at Old Trafford - their first in the PL by a margin of 4+ goals since August 2021.
A sixth defeat in 13 games leaves the Toffees precariously close to the relegation zone meanwhile, with just two points separating themselves and Wolves in 18th.