Carlo Ancelotti promised Everton would be vastly improved at Villa Park from the performance against the same opponents 11 days ago.
And the Italian’s players ensured their manager could maintain a reputation as a man of his word.
Everton recorded their fourth successive away clean sheet and their ninth of the season.
That Goodison defeat by Villa is the only loss in seven Premier League games.
But, try as they might, especially after half-time when Everton grew as an attacking proposition, Ancelotti’s team couldn’t force a winner.
The substitutions were positive and Andre Gomes twice had opportunities after arriving on 67 minutes.
Dominic Calvert-Lewin’s header following a trademark Lucas Digne delivery with three minutes remaining was repelled by a reaction Emiliano Martinez stop .
And Calvert-Lewin was denied again right at the end when Tyrone Mings intercepted Richarlison’s low delivery.
One significant tick in the plus column for Everton was Abdoulaye Doucoure's return following a 10-week layoff. He completed 90 minutes and looked like he'd never been away.
The upshot is Everton have 56 points, level with Tottenham Hotspur in seventh, and are two behind West Ham United, who were fifth before Liverpool went to Manchester United on Thursday night.
Everton play Sheffield United at Goodison Park on Sunday and need to win.
In minute 17, as Mings launched himself at a Douglas Luiz delivery, an opening goal seemed inevitable.
The chance came at the end of a flurry of home pressure. Digne defended well at the back post to frustrate Bertrand Traore – the biggest threat in claret and blue until this point – after Matt Targett lifted a cross from the left.
Calvert-Lewin headed out the resultant corner but Brazilian Luiz was first to the loose ball, dashing forwards to cross.
Mings had a clear sight of goal with the diving header from eight yards but was wide of Jordan Pickford’s left post with his attempt.
Everton’s first effort came from Calvert-Lewin but the striker had it all on trying to generate meaningful power from Seamus Coleman’s cross and the save was easy for Martinez.
Ancelotti’s team were playing in the amber and blue away kit we’ve not seen a huge amount this season.
But they were immediately recognisable as the tough bunch that’s ground out away win after away win in this difficult-to-interpret campaign.
The midfield was a heavily-populated, fractious battleground, and when the hosts crossed the halfway line they typically had eight defensive bodies between them and the goal.
Villa’s increasing frustration was evident when Traore was confronted by three of those amber shirts on a run into the box two minutes before half-time.
He went to ground, too easily in the view of Martin Atkinson, the referee, and was booked.
In their previous two away games, at Arsenal and West Ham United, Everton capped their obduracy with a winning goal when chances were at a premium.
And the creation of opportunities represented the toughest ask here.
The best-looking opening of the first half came when Digne – following Coleman’s second booming right-to-left ball in quick succession – sent over a cross that was impossible to defend.
Martinez, wisely, wanted nothing to do with it.
Calvert-Lewin, however, speeding to the back post, couldn’t achieve contact.
Gylfi Sigurdsson got hold of a free-kick after Matty Cash fouled Richarlison but it was directed straight down Martinez’s throat.
And a fluid move, which began with Doucoure firing a ball right for Coleman and went through Digne, Sigurdsson and Allan, climaxed with Richarlison dragging off target.
Traore had the game’s first shot on target, after 11 minutes, but it was straightforward for Pickford, again the epitome of composure and authority on his fifth successive start in Everton’s goal.
Anwar El Ghazi, matchwinner when the sides met 11 days ago, fired over on the run.
There was a nice little vignette when the rapid Traore tried the push-and-run method to get past Ben Godfrey on Everton’s left.
Trying to beat Godfrey for pace, the former Chelsea player learned, is the very definition of a fool’s errand.
Villa did make some headway down the opposite flank after 26 minutes when Keinan Davis escaped to flash a ball across the face of goal.
The striker was aghast to look up and see Barkley was his only teammate in the box – and, even then, only just arriving and nowhere near the delivery.
Calvert-Lewin went a fraction early and was flagged offside after being denied one-on-one by Martinez following the restart.
The forward timed his run the next time, fastening on to Doucoure’s pass but discovering the angle was too tight to defeat Martinez.
Everton were attacking with more conviction now and from all angles.
Coleman’s hybrid full-back, wing-back role includes licence to come infield.
Indeed, there were occasions at West Ham four days ago when he seemed to operate as a third central midfielder.
Moving inside, here, the Everton captain was upended by John McGinn, 30 yards out.
Sigurdsson opted for guile with the dead ball, drifting it over Villa’s backline for Godfrey, running round the back.
The defender hooked the ball into the middle where it was met by Martinez’s huge left palm.
Pickford beat out an El Ghazi free-kick before Ancelotti introduced his first substitute in the shape of Gomes, replacing Sigurdsson.
And within 60 seconds of coming on, Gomes had a sight of goal. The Portuguese controlled a pass from Richarlison along the perimeter of the box and feinted to deceive Luiz.
The shot with his left foot was too high, however.
Alex Iwobi followed soon after, on for Coleman, as Everton showed their hand.
Dean Smith, the Aston Villa manager, played his joker in the meantime, sending on the exceptional Jack Grealish for Traore.
Gomes fired against the feet of Ahmed El Mohamady – on late in the first half for the injured Matty Cash – after striding forwards to meet a Richarlison cut back.
Then the big chance. We’ve seen it countless times, Digne scurrying down the left and hanging up a ball for Calvert-Lewin.
The header was good but well saved by Martinez. Doucoure crashed the rebound into the turf, inadvertently finding Richarlison, who couldn’t control his header.
Mings slid in to prevent Richarlison’s cross reaching Calvert-Lewin in front of goal at the beginning of three added minutes.
Dynamic Doucoure's Welcome Return
Carlo Ancelotti was grateful to have Abdoualye Doucoure available again at Villa Park, admitting the Frenchman’s energy was hard to replace during an enforced absence.
Doucoure is an endangered species in modern football, a genuine box-to-box midfielder in an age of ‘holders and pivots, sixes and eights and number 10s’.
The rangy 28-year-old’s leggy stride eats up the turf and he used that attribute to recover and prevent Anwar El Ghazi feeding in an early cross.
Doucoure was back 10 weeks to the day after he fractured a foot in a 1-0 win at West Bromwich Albion, a result that lifted Everton to fifth.
And with his side aiming for another meaningful victory in the West Midlands – the carrot was a three-place jump to sixth – Ancelotti sensed the right moment for Doucoure to return.
The former Watford player sat on the bench at West Ham United on Sunday and plainly savoured the chance to get his boots muddy here.
In tandem with Allan, Doucoure kept Villa’s midfield honest. Douglas Luiz found to his cost midway through the opening half this wasn’t a night to take liberties on the ball.
Doucoure had particular focus on Ross Barkley, never straying far from the ex-Everton playmaker when Villa advanced.
The idea was to stop the ball getting to Barkley’s feet after the Englishman and a handful of his colleagues enjoyed too much space at Goodison Park 11 days ago.
Barkley was stifled and began moving wide to try to escape Everton’s imposing number 16. He had little success and went off with 25 minutes remaining.
Docuoure moved the ball at speed, aiming to transfer possession from congested areas to teammates in positions start attacks.
As Everton grew more adventurous after half-time Doucoure, showing no signs of flagging, followed suit.
He began appearing on the fringes on Villa’s area and prodded through one ball to release Dominic Calvert-Lewin for a shot.
The same two players combined six minutes from the end. Doucoure, who was getting in Luiz’s face on Villa’s 18-yard line soon after, sprang Calvert-Lewin, who got to the ball before Emiliano Martinez but couldn’t keep it in play.
Obdurate Blues Going Home For Away-Day Reward
Everton climbed back above Arsenal with this point which keeps them firmly in the pack hunting European football.
It is in keeping with this topsy-turvy campaign that progress was achieved – albeit a win was the objective – with a another strong away display.
This was a fourth straight clean sheet on the road and Everton have 37 points from their 18 away games, a return of more than two per match.
Additionally, they have recorded nine away shutouts, equalling the Club’s Premier League-era record from 2008/09.
But for Everton to make full capital on this point, they must alight on a way of succeeding back at Goodison Park.
Everton are likely to need wins from both remaining home matches to gain tangible reward for a consistently stellar effort on their travels.
The meeting with Villa 11 days ago, a 2-1 home defeat, sandwiched by pressure victories at Arsenal and West Ham United, encapsulates why Everton aren’t already planning for a European campaign.
God willing, Sheffield United’s visit on Sunday will be the last Goodison Park game without fans.
Ancelotti’s team have been measured and clinical away, repeatedly inflicting death by a thousand cuts.
Emotion and instinct would normally govern performances in front of a partisan Goodison crowd but Everton – in common with multiple Premier League counterparts – have struggled to build up a head of steam in an eerily quiet home stadium.
Mercifully, this isn’t an issue that needs addressing for the long term.
But after laying the groundwork in the capital and second city this week, Everton’s chances of European football could rest on what they summon back on familiar turf in three days’ time.