Ollie Watkins broke the deadlock five minutes into the second half after a Jarrad Branthwaite mistake allowed Morgan Rogers to tee him up.
The Blues remain a point away from the Premier League’s relegation zone following their third successive loss and a first under their new manager.
Here were the key talking points from Goodison Park:
Moyes receives a crash course
By personal admission, David Moyes knew he would be encountering a very different Everton to the one he walked away from just under 12 years ago.
Given the contrast between what he left behind and what he subsequently inherited, his homecoming was never likely to begin on a similar footing.
The feelgood factor eluded him a second time around, as did a quickfire opener from an unlikely source and, most of all, a much-needed victory.
Not even the enticing prospect of Goodison Park under the lights could spare the new manager the ordeal of this unhappy return against Aston Villa..
But the Blues’ third straight Premier League loss will have been an eye-opening experience for Moyes as he battles against relegation once more.
If he was under any illusions of the task ahead, the players who failed so embarrassingly under Sean Dyche swiftly disabused him of that notion.
Jack Harrison and Abdoulaye Doucoure singled themselves out as the worst offenders but, in truth, few in the royal blue shirt could claim any vindication.
Moyes prides himself on being a good judge of character and doubtless took on board some important lessons about his side’s ongoing deficiencies.
DCL takes another step back
Few players were namechecked in Moyes’ inaugural address on Monday but Dominic Calvert-Lewin proved to be an exception to that particular rule.
The Everton manager forecast that the striker could ‘make a big difference’ in their latest bid to beat the drop if he finally rediscovered his scoring boots.
After a 15th game without finding the target, however, Calvert-Lewin took another step back despite appearing brighter than on previous occasions.
A well-timed run to meet Vitalii Mykolenko’s clever ball over the top should have broken that recent duck but saw him flash a chested volley wide.
His follow-up attempt from a Harrison chip fared little better with an awkward hooked effort which allowed Boubacar Kamara an easy goal-line clearance.
Even possible redemption in front of the Gwladys Street End failed to favour Calvert-Lewin as he blazed Jesper Lindstrom’s cross over from close range.
With Beto still flattering to deceive and Armando Broja seemingly destined for an early return to Chelsea, the 27-year-old remains Everton’s leading option.
Yet as his contract rapidly ticks down and goals remain hard to come by, Calvert-Lewin has entered the ‘shape up or ship out’ phase at Goodison.
Goodison gets back on board
Another matchday ending in chastening defeat is not how most Evertonians envisaged their increasingly diminishing final season at Goodison playing out.
There could be more on the horizon, too, with Tottenham’s resurgent display elsewhere on Wednesday night teeing up their upcoming visit to Merseyside.
While these remain trying times, there were signs inside the Grand Old Lady that its long-suffering devotees are already back on board under Moyes.
In recent weeks, this game would have previously been a bigger walkover for a Villans side who had lost their last five Premier League away games.
But even as the visitors racked up chance upon chance in the early stages, and went on to break the deadlock, supporters’ backing never wavered.
At times under Dyche, there would have been an air of resignation from the second their team were facing an uphill battle due to his negative style.
Small steps, undoubtedly, but fans have already heeded Moyes’ message.
