Chris Wilder's side, back in top flight for the first time since relegation in 2007, are unbeaten away from home since mid-January and this performance demonstrated why that was the case.
Organised, disciplined, decisive and committed to a game plan – almost everything their hosts were not having gone behind vastly against the run of play.
Marco Silva's team were previously unbeaten at home since February but having failed to press home their first-half advantage the latter stages of the game bordered on the chaotic in a hastily thrown-together formation as they tried to salvage something after last week's chastening defeat at Bournemouth.
It was in stark contrast to the way the visitors operated, never once deviating from what Wilder had asked them to do despite seeing little of the ball.
Silva opted for Moise Kean up front but he looked like he was trying too hard to score, having not found the net since April 13, although he was not presented with many opportunities.
Everton's domination of possession led to little in the way of chances with the final pass often wayward or intercepted and for seasoned Goodison-goers what came next was all too familiar.
Goalkeeper Jordan Pickford came to claim Oliver Norwood's inswinging corner, United's first, and although there was shoulder-to-shoulder contact with Callum Robinson there was not enough, VAR ultimately decided, to warrant a foul.
The ball going in off the apparently startled Mina's shoulder merely added to Everton's embarrassment.
The unmarked Richarlison epitomised Everton's weakness in front of goal with a poor header 10 yards out.
Whereas United's flexible back five encouraged their central defenders to regularly join the attack, Everton needed one of their holding midfielders of Morgan Schneiderlin and Fabian Delph to occasionally break the line.
Silva rectified that 10 minutes into the second half when he dropped Gylfi Sigurdsson into a deeper midfield role, switching to 4-4-2 after bringing on Alex Iwobi and Cenk Tosun for Bernard and Schneiderlin.
The hosts were re-energised and Wilder sent on former Toffees captain Phil Jagielka, who finally got to say goodbye to Goodison Park properly having left in the summer after 12 seasons, to add his vast experience to the rearguard action.
However, Everton's haphazard 3-1-3-3 set-up only seemed to produce confusion and not penetration with the visitors' tried-and-tested organisation allowing them to profit.
That prompted hundreds of home fans to head for the exit and suddenly next week's Carabao Cup tie in Sheffield – against Wednesday – takes on unnecessarily greater significance for Silva.