The Barclays Premier League’s established “big four” have been unchallenged for so long that doubts continue to be harboured about Everton and Aston Villa’s chances of claiming a seat at the top table of English football this season, but if events at Goodison Park yesterday were anything to go by, such reservations appear increasingly misguided.

Everton booked their place in the FA Cup quarter-finals for the first time since David Moyes’s arrival as manager almost seven years ago, but as deserved as their victory was, Villa more than played their part during another absorbing tie that showcased all that is good about these two teams — courage, character, industry and invention — and they are qualities that should have Arsenal and Chelsea feeling more than a little anxious.

As Moyes acknowledged, this should have been a game too far for Everton, but then their ability to dig deep and go that extra mile is becoming one of their greatest strengths. Villa were without Gareth Barry, their captain, who was suspended, and the injured Emile Heskey. Both were missed, but Martin O’Neill’s options seemed plentiful compared with his Everton counterpart.

On any other day, Moyes would probably have chosen to rest Tim Cahill and Tim Howard, but with eight senior players unavailable through injury or suspension, it was not a luxury available to him.

Cahill was jet-lagged after another exhausting midweek trip to play for Australia in Japan while Howard, the goalkeeper, slept with an ice-bag attached to his thigh on Saturday night after suffering an injury on duty with the United States, but you would never have known.

With Everton leading 2-1, Howard tipped aside John Carew’s volley magnificently in the 61st minute, before Cahill put the result beyond doubt to cap another outstanding display as a makeshift centre forward. Sporting a black armband, he dedicated his goal to the 181 victims of the bushfires that tore through Victoria last week.

“It puts it all in perspective,” he said. “It was only something little, but I was just happy that I was able to contribute.”

Everton have not fared too well in cup competitions under Moyes, which might help to explain why the manager is refusing to get too carried away, but after hugely impressive victories over Liverpool in the previous round and now Villa, the Merseyside club should prove a handful for anyone. “If we keep in good form and keep playing like we have in the past few months we have a chance \,” Mikel Arteta, the midfield player, said.

Villa had not been beaten domestically for more than three months and had won eight away games during that period, including a dramatic 3-2 league success at Goodison Park in December, but Everton refused to be cowed by such statistics and had taken, squandered and regained the lead after 24 rollercoaster minutes.

Jack Rodwell put Everton in front after four minutes. Craig Gardner handled Cahill’s header on the line, but Martin Atkinson, the referee, played the advantage, allowing Rodwell to scoop in the loose ball for his first goal for the club.

When Villa equalised four minutes later, Tony Hibbert upending Gabriel Agbonlahor and James Milner scoring from the penalty spot, Moyes must have been wishing that Atkinson had awarded Everton a penalty and sent off Gardner rather than allow the goal, but it was not long before his team were in front again.

Victor Anichebe, restored to the starting line-up after an unseemly spat with Moyes and playing as though his Everton career depended on it, tore a hole through the middle of the Villa defence before being tripped by Steve Sidwell and Arteta scored from the spot.

Moyes had broken with his conventional 4-4-1-1 formation by switching to a fluid 4-3-2-1 and it paid dividends. Hibbert and Leighton Baines were occasionally exposed, but Arteta and Rodwell, who will sign a five-year deal with the club this week, a month before his 18th birthday, excelled.

Villa had three chances to at least draw level before Cahill scored Everton’s third, but Agbonlahor and Sidwell made a hash of inviting headers while Carew was denied by Howard.

With CSKA Moscow to play in the Uefa Cup on Wednesday before the visit of Chelsea in the league on Saturday, Villa are likely to face more stiff examinations this week, but like Everton, they are clearly relishing the fight.

Everton (4-3-2-1): T Howard 7 - A Hibbert 5, P Jagielka 7, J Lescott 7, L Baines 6 - P Neville 7, M Arteta 8, J Rodwell 7 - D Gosling 6, T Cahill 8 - V Anichebe 7. Substitutes: J Yobo (for Anichebe, 88min), S Castillo (for Arteta, 90). Not used: C Nash, A van der Meyde, L Jacobsen, J Baxter, J Wallace.

Aston Villa (4-4-2): B Friedel 6 - C Gardner 5, Z Knight 6, C Davies 6, L Young 5 - J Milner 7, S Petrov 6, S Sidwell 5, A Young 7 - J Carew 5, G Agbonlahor 6. Substitutes: N Delfouneso (for Sidwell, 83min). Not used: B Guzan, M Harewood, M Salifou, N Shorey, M Albrighton, S Lowry.

Referee: M Atkinson Attendance: 35,439

Teenage kicks all the rage at Goodison

After a 17-year-old supplied the Everton goal that knocked Liverpool out of the FA Cup, a 19-year-old scored yesterday to set them on their way to victory over Aston Villa. Lacking money and a deep squad, Everton have turned to teenagers occasionally this season. Dan Gosling netted the derby winner at Goodison Park and Jack Rodwell was on target yesterday, but they have not been Everton’s most youthful performers. Jose Baxter was 16 years and 191 days when he became the club’s youngest player by appearing on the opening day of the campaign.

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