David Moyes suffered defeat on his return as Everton manager after Ollie Watkins' second-half strike secured a hard-fought 1-0 victory at Goodison Park.
Dominic Calvert-Lewin lifted a huge stoppage-time chance over the bar as hopes of a dramatic equaliser for the hosts evaporated, with Villa ending their five-game away losing streak in the Premier League.
Watkins, who missed a glorious chance in the first half, made no mistake as he raced onto Morgan Rogers' pass to slide his shot beneath Jordan Pickford for his ninth league goal of the season.
The result ignites Villa's push for a Champions League place as they move up to seventh in the Premier League, three points off fourth-placed Newcastle. Everton, meanwhile, stay in 16th - just a point outside the relegation zone.
Moyes' task laid bare as Everton fire blanks again
Back in 2002, the year Moyes first walked the corridors of the tunnel up to the dugout at Goodison Park, Everton were celebrating becoming the first English club to play 100 seasons in the top division.
Now, as he embarks on series two, his first test came in what is the most-played top-flight fixture in English football between the two most successful founder members of the world's first football league.
But Moyes will know that for that proud record to be extending into another season, he must reinvigorate an ageing squad and a place that had gone stale under his predecessor, Sean Dyche.
Calvert-Lewin had been urged to stand up and be the front man of Moyes' second coming, with the striker having not scored since the reverse fixture at Villa Park back in August.
He had two presentable opportunities in the first half to break the deadlock, with his second effort cleared off the line by the excellent Boubacar Kamara with the ball caught underneath his feet.
His opportunity at the end summed up his season. The pass to him from Jesper Lindstrom was not perfect as it bobbled his way but he ought to have hit the target. He is now without a goal in his last 16 games.
Abdoulaye Doucoure also had an effort comfortably saved from Vitaliy Mykolenko's cross. There was plenty of endeavour after Watkins' decisive strike but few chances and ultimately not enough quality to deny Villa their first away league win since October.
Clinical Villa pounce on Pickford indecision
Everton have now failed to score in nine of their last 11 league games - with just one goal in open play during that time. They are without a goal at all in over five hours but Villa arrived with their own problems to solve having lost each of their last five away league games, conceding at least twice on each occasion.
For Watkins, it was a night of atonement. The striker was gifted a glorious chance in the first half as he ran onto Ashley Young's poor backpass but his shot veered wide of the post.
By then, Rogers had already drawn a fine save from Pickford but the England No 1 showed indecision at the crucial moment six minutes after the restart.
Several 50-50 challenges were missed by players in blue higher up the pitch before Rogers was allowed to break and feed his team-mate Watkins for a low finish, with the Everton goalkeeper unsure of his positioning.
It was the fourth time Watkins has combined with Rogers this season and on this occasion it was enough to seal all three points as Moyes' return ended in defeat.
In truth, Villa did not produce much in the second half beyond their goal. Emiliano Martinez and Tyrone Mings reverted to good game management, with the rub of the green favouring Unai Emery's side when Jacob Ramsey blocked Jarrad Branthwaite's shot from a half-cleared corner.
Given Everton's attacking problems, Watkins' strike was always likely to be enough.
"I'm very happy," said Emery. "It was a tough match. We played 90 minutes and competed very well. We had some clear chances in the first half and we tried to push and take even more control in the second but we couldn't, but we scored.
"This victory is very important. We have started the year winning at home, in the Premier League and in the FA Cup. Away, we were in a bad spell and had to break it."
Villa extend fine Toffees record - Opta stats
